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Computer System Architecture
M. Morris Mano
정보통신공학과

이 명 의(A-405)

melee@kut.ac.kr

Computer System Architecture

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-2

Class Overview
Contents
Chap. 1 Digital Logic Circuits

The fundamental knowledge needed for the design of digital systems constructed with individual
gates and flip-flops.

Chap. 2 Digital Components
The logical operation of the most common standard digital components(Decoders, Multiplexers,
Registers, Counters, and Memories).
These digital components are used as building blocks for the design of larger units(Mano
Machine).

Chap. 3 Data Representation
Various data types found in digital computers are represented in binary form in computer
registers.

Chap. 4 Register Transfer and Microoperations
A register transfer language is used to express microoperations in symbolic form.
Symbols are defined for arithmetic, logic, and shift microoperations.
To show the hardware design of the most common microoperations, a composite arithmetic logic
shift unit is developed.

Chap. 5 Basic Computer Organization and Design
The organization and design of a basic digital computer(Mano Machine).
Register transfer language is used to describe the internal operation of the computer.
By going through the detailed steps of the design presented in this chapter, the student will be
able to understand the inner workings of digital computers.
Computer System Architecture

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-3

Class Overview
Chap. 6 Programming the Basic Computer
The 25 instructions of the basic computer to illustrate techniques used in assembly language
programming.
Programming examples are presented for a number of data processing tasks.
The basic operations of an assembler are presented to show the translation from symbolic code
to an equivalent binary program.

Chap. 7 Microprogrammed Control
Introduction to the concept of microprogramming.
A specific microprogrammed control unit is developed to show by example how to write
microcode for a typical set of instructions.
The design of the control unit is carried-out in detail.

Chap. 8 Central Processing Unit
CPU as seen by the user(ISA).
General register organization, the operation of memory stack, variety of addressing modes,
instruction format.
The Reduced Instruction Set Computer(RISC) concept.

Chap. 9 Pipeline and Vector Processing
The concept of pipelining is explained(Pipeline can speed-up processing).
Both arithmetic and instruction pipeline is considered
Vector processing is introduced(Example: Floating-point operations using pipeline procedures)

Computer System Architecture

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-4

Class Overview
Chap. 10 Computer Arithmetic

Arithmetic algorithms for digital hardware implementation(addition, subtraction, multiplication,
and division).

Chap. 11 Input-Output Organization
Computer communication with input and output devices.
I/O interface units are presented to show the way that the processor interacts with external
peripherals.
4 modes of transfer : Programmed I/O, Interrupt initiated transfer, direct memory access, and
IOP.

Chap. 12 Memory Organization
The concept of memory hierarchy : cache memory, main memory, auxiliary memory
The organization and operation of associative memories is explained in detail.
Memory Management Unit : physical address and logical address mapping

Chap. 13 Multiprocessors
A multiprocessor system is an interconnection of two or more CPUs.
Various interconnection structures are presented : Time-shared common bus, Multiport Memory,
Crossbar Switch, Multistage Switching Network, Hypercube Interconnection
Interprocessor Arbitration : System bus, Serial Arbitration Procedure, Parallel Arbitration
Logic, Dynamic arbitration Algorithms.
Interprocessor Communication and Synchronization : Mutual Exclusion with a Semaphore
Cache coherence
Computer System Architecture

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-5

Class Overview
All 3 subjects associated with computer hardware in this book
Computer Organization(Chap 1, 2, 3, 4)

H/W components operation/connection.
Various digital components used in the organization and design of digital computer.

Computer Design(Chap 5, 6, 7)
H/W Design/Implementation.
The steps that a designer must go through to design and program an elementary
digital computer(Chap. 6 : program = ISA)

Computer Architecture(Chap 6, 8, 9, 11, 12)
Structure and behavior of the computer as seen by the user
» Information format, Instruction set, memory addressing : S/W = ISA
» CPU, I/O, Memory : H/W

Chapter in detail
»
»
»
»

Computer System Architecture

Chap. 6 : ISA
Chap. 8 and 9 : CPU
Chap. 11 : I/O
Chap. 12 : Memory

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-6

Class Overview
What is “Computer Architecture”?
- Hennessy and Patterson, Computer Organization and Design(1990)

Computer Architecture
Instruction Set Architecture (ISA) : S/W
Machine Organization : H/W and Design

“ISA(Instruction Set Architecture)”?
the attributes of a system as seen by the programmer, i.e., the conceptual structure and
functional behavior, as distinct from the organization of the data flows and controls, the
logic design, and the physical implementation.

- Amdahl, Blaaw, and Brooks(1964)
Instructions, Addressing modes, Instruction and data formats, Register

“Machine Organization”?
CPU(Control & Data path), Memory, Input/Output

Computer System Architecture

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
Class Overview

1-7

First Course in Computer Hardware
Learn how a computer actually works
Build the “Mano Machine”
Learn one computer in detail, others are mastered easily.
Homework:
Solve the even number of problems
Due at the beginning of the next class

Optional “Mano Machine” Design Report
Grade:
Homework(20%)
Optional Report(10%)
Mid/Final Exam(each 30%)
Class Participation(10%)

Lecture Notes: http://microcom.kut.ac.kr

Computer System Architecture

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
8 Student Types

1-8

Insecure: 25 %
Silent: 20 %
Independent: 12 %
Friendly: 11 %
Obedient: 10 %
Heroic: 9 %
Critic: 9 %
Unmotivated: 4 %
- Michigan State University

Computer System Architecture

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-9

1-1 Digital Computers
Digital Computer = H/W + S/W
Digital
implies that the information in the computer is represented
by variables that take a limited number of discrete values.
the decimal digits 0, 1, 2,….,9, provide 10 discrete values,
but digital computers function more reliably if only two
states are used.
because of the physical restriction of components, and
because human logic tends to be binary(true/false, yes/no),
digital component are further constrained to take only two
values and are said to be binary.

Bit = binary digit : 0/1
Program(S/W)

Application S/W

API
Operating System

ROM BIOS

A sequence of instruction
S/W = Program + Data

Computer H/W

» The data that are manipulated by the program constitute the
data base

Application S/W = DB, word processor, Spread Sheet
System S/W = OS, Firmware, Compiler, Device Driver
Computer System Architecture

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-10

1-1 Digital Computers

continued

Computer Hardware(H/W)
CPU
Memory
Program Memory(ROM)
Data Memory(RAM)

Memory

I/O Device
Interface: 8251 SIO, 8255 PIO,
6845 CRTC, 8272 FDC, 8237
DMAC, 8279 KDI

CPU

Input Device: Keyboard, Mouse,
Scanner

Output Device: Printer, Plotter,
Display

Storage Device(I/O): FDD, HDD,
MOD

Input
Device

Interface
or IOP

Output
Device

Figure 1-1 Block Diagram of a digital Computer

Computer System Architecture

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-11

1-2 Logic Gates
ADC(Analog to Digital Conversion)
Signal

Physical Quantity
V, A, F, 거리

0 : 0.5v

Binary Information
Discrete Value

1 : 3v

Gate
The manipulation of binary information is done by logic circuit called
“gate”.
Blocks of H/W that produce signals of binary 1 or 0 when input logic
requirements are satisfied.
Digital Logic Gates : Fig. 1-2
AND, OR, INVERTER, BUFFER, NAND, NOR, XOR, XNOR

x
y

Computer System Architecture

xy

x
y

xy

Chap. 1 Digital Logic Circuits

x

x

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-3 Boolean Algebra

1-12

Boolean Algebra
Deals with binary variable (A, B, x, y: T/F or 1/0) +
logic operation (AND, OR, NOT…)

Boolean Function: variable + operation
F(x, y, z) = x + y’z

George Boole
Born: 2 Nov 1815 in Lincoln,
Lincolnshire, England

Died: 8 Dec 1864 in Ballintemple,
County Cork, Ireland

Computer System Architecture

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-13

1-3 Boolean Algebra
Boolean Function: variable + operation
F(x, y, z) = x + y’z

Truth Table: Fig. 1-3(a)

Logic Diagram: Fig. 1-3(b)

Relationship between a function
and variable

Algebraic Expression
Logic Diagram(gates로 표현)

x y z

2n Combination
Variable n = 3

Computer System Architecture

F

0
0
0
0
1
1
1
1

0
1
0
0
1
1
1
1

0
0
1
1
0
0
1
1

0
1
0
1
0
1
0
1

x
y

F

z

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-14

Purpose of Boolean Algebra
To facilitate the analysis and design of digital circuit

Boolean function = Algebraic form = convenient tool
Truth table (relationship between binary variables : Fig 1-3a) Algebraic form
Logic diagram (input-output relationship : Fig. 1-3b) Algebraic form
Find simpler circuits for the same function : by using Boolean algebra rules

Boolean Algebra Rule : Tab. 1-1
- Operation with 0 and 1: x + 0 = x , x + 1 = 1 , x • 1 = x , x • 0 = 0
- Idempotent Law: x + x =x , x • x = x
- Complementary Law: x + x' = 1 , x • x' = 0
- Commutative Law: x + y = y + x , x • y = y • x
- Associative Law: x + (y + z) = (x + y) + z , x • ( y • z) = (x • y) • z
- Distributive Law: x • ( y+ z) = (x • y) + (x • z) , x + (y • z) = (x + y) • (x + z)
- DeMorgan's Law: (x + y)' = x' • y’ , (x • y )’ = x’ + y’
General Form: (x1 + x2 + x3 + … xn)' = x1' • x2' • x3' • … xn’

( A U B ) c = Ac I B c

(x1 • x2 • x3 • … xn) ' = x1' + x2' + x3' + … xn’
Computer System Architecture

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-15

[예제]

Fig. 1-6(a)

[예제]

F= AB’ + C’D + AB’ + C’D
= x + x (let x= AB’ + C’D)
=x
= AB’ + C’D

F= ABC + ABC’ + A’C
= AB(C + C’) + A’C Fig. 1-6(b)
= AB + A’C
1 inverter, 1 AND gate 감소

Fig. 1-4 2 graphic symbols for NOR gate
x
y
z

(x+y+z)’

x
y
z

(a) OR-invert

x’ y’z’ =(x+y+z)’

(b) invert-AND

Fig. 1-5 2 graphic symbols for NAND gate
x
y
z

(xyz)’

(a) AND-invert
Computer System Architecture

x
y
z

(x’+y’+z’) = (xyz)’

(b) invert-OR
Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-4 Map Simplification

1-16

Karnaugh Map(K-Map)
Map method for simplifying Boolean expressions

Minterm / Maxterm
Minterm : n variables product ( x=1, x’=0)
Maxterm : n variables sum (x=0, x’=1)

2 variables example
x
0

y
0

Minterm
x'y'
m0

Maxterm
x +y
M0

0

1

x'y

m1

x + y'

M1

1

0

x y'

m2

x'+ y

M2

1

1

x y

m3

x'+ y'

M3

F = x’y + xy
m1

M0 • M1 • M2 • M3

m3

= Σ(1,3)
= Π (0,2)
Computer System Architecture

m0 + m1 + m2 + m3

( m1 +

m3 )

(Complement = M0 •

M2 )

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-17

Map
3 variables

2 variables
B

0
A

C

B

1

2

4 variables

3

0

3

5

7

0

6
A

C

5 variables

1

3

2

4

2

4

A

1

5

7

6

12 13 15 14
8

C

B

9

11 10
D

0

3

8
A

1

2

6

7

5

4

9

11 10 14 15 13 12

B

24 25 27 26 30 31 29 28
16 17 19 18 22 23 21 20
E

Computer System Architecture

D

F

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-18

[예제] F= x + y’z
(2) F ( x , y , z ) = Σ(1,4,5,6,7 )

(1) Truth Table
x
0

y
0

z
0

F
0

Minterm

0

0

1

1

m1

0

1

0

0

m2

0

1

1

0

m3

1

0

0

1

m4

1

0

1

1

m5

1

1

0

1

m6

1

1

1

1

m7

(3)

Computer System Architecture

y

m0
0

x

1

3

2

4

5

7

6

z

F= x + y’z

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-19

Adjacent Square
Number of square = 2n (2, 4, 8, ….)
The squares at the extreme ends of the
same horizontal row are to be
considered adjacent

1

3

2

4

5

7

6

0

1

3

2

4

The same applies to the top and
bottom squares of a column

0

5

7

6

12

13

15

14

8

9

11

10

Groups of combined adjacent squares
may share one or more squares with
one or more group

Computer System Architecture

Chap. 1 Digital Logic Circuits

0
0

1

3

4

5

7

0

1

3

5

7

5

7

6

13

15

14

9

11

10

2

4

2

12

6

3

4

2

1

8

The four corner squares of a map must
be considered to be adjacent

6

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-20

B

[예제] F ( A, B, C ) = Σ(3,4,6,7)
0

F=AC’ + BC

A

3

2

4

5

7

6

0
A

1

3

2

4

5

7

6
C

C

[예제] F ( A, B, C , D ) = Σ(0,1,2,6,8,9,10)
0

Product-of-Sums Simplification
F ( A, B, C , D ) = Σ(0,1,2,5,8,9,10)

3

2

5

7

6

12

13

15

14

8

A

1

4

F=B’D’ + B’C’ + A’CD’

F=B’D’ + B’C’ + A’C’D

B

C

[예제] F ( A, B, C ) = Σ(0,2,4,5,6)
F=C’ + AB’

1

9

11

10
C

D

Sum of product

0

A

Product of Sum
Computer System Architecture

Chap. 1 Digital Logic Circuits

1

3

2

4

F’=AB + CD + BD’(square marked 0’s)
F’’(F)=(A’ + B’)(C’ + D’)(B’ + D) 전개

B

5

7

6

12

13

15

14

8

9

11

10

B

D
© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-21

NAND Implementation
Sum of Product : F=B’D’ + B’C’ + A’C’D
B’
D’
C’
A’
D

NOR Implementation
Product of Sum : F=(A’ + B’)(C’ + D’)(B’ + D)
A’
B’
C’
D’

D’

B

Don’t care conditions

0

F(A,B,C)=Σ(0, 2, 6), d(A,B,C)= Σ(1, 3, 5)
F=A’ + BC’= Σ(0, 1, 2, 3, 6)
Computer System Architecture

Chap. 1 Digital Logic Circuits

A

4

X
X

1
5

X

3

2

7

6

C
© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-22

1-5 Combinational Circuits
Combinational Circuits

in

Combinational
Circuits
(Logic Gates)

...

i0
i1

...

A connected arrangement of logic gates with a set of inputs and outputs
Fig. 1-15 Block diagram of a combinational circuit

f0
f1
fm

Analysis
Logic circuits diagram

Design(Analysis의 반대)

Boolean function or Truth table
Experience

1. The Problem is stated
2. I/O variables are assigned
3. Truth table(I/O relation)
4. Simplified Boolean Function(Map 과 Boolean 대수 이용)
5. Logic circuit diagram

Computer System Architecture

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-23

Design Example : Full Adder
1. Full adder is a combinational circuits that forms the arithmetic sum of
three input bit (Carry considered)
2. 3 Input(x, y, z), 2 Output(S: sum, C: carry)
3. Truth Table
4. Simplification
x
0
0
0
0
1
1
1
1

Input
y
0
0
1
1
0
0
1
1

z
0
1
0
1
0
1
0
1

Output
C
S
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1

y

y

0

3

5

7

6

z

C= xy’z + x’yz + xy
=z(xy’ + x’y) + xy
=z(x ⊕ y) + xy

5. Logic circuit diagram
x
y

c

z
s
Computer System Architecture

0

2

4

x

1

Chap. 1 Digital Logic Circuits

x

1

3

2

4

5

7

6

z

S=xy’z’ + x’y’z + xyz + x’yz’
= z’(xy’ + x’y) + z(x’y’ + xy)
= z’(x ⊕ y) + z(x ⊕ y)’
=a’b + ab’ (let a=z, b=x ⊕ y)
=x ⊕ y ⊕ z
(x ⊕y)’=(xy’+x’y)’
=(x’+y)(x+y’)
=x’x+x’y’+xy+yy’
=x’y’+xy
© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-24

1-6 Flip-Flops

Combinational Circuit = Gate
Sequential Circuit = Gate + F/F

Flip-Flop

The storage elements employed in clocked sequential circuit
A binary cell capable of storing one bit of information

D(Data) F/F

SR(Set/Reset) F/F
S

R

SET

CLR

Q
Q

S
0
0
1
1

R
0
1
0
1

Q(t)
0
1
?

Q(t+1)
no change
clear to 0
set to 1
Indeterminate

J

K

CLR

Q
Q

J
0
0
1
1

K
0
1
0
1

CLR

Q
D
0
1

Q

0
1

Q(t+1)
clear to 0
set to 1

“no change” condition이 없다 : Q(t+1)=D

T(Toggle) F/F

Q(t+1)
Q(t) no change
0
clear to 0
1
set to 1
Q(t)' Complement

JK F/F is a refinement of the SR F/F
The indeterminate condition of the SR
type is defined in complement
Computer System Architecture

SET

해결방법 : 1) Disable Clock
2) Feedback output into input p.52

JK(Jack/King) F/F
SET

D

T

SET

CLR

Q

T
0
1

Q(t+1)
Q(t) no change
Q'(t) Complement

Q

T=1(J=K=1), T=0(J=K=0) 이면 JK F/F
수식 표현 : Q(t+1)= Q(t) ⊕ T xor

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-25

Positive clock transition

Edge-Triggered F/F
State Change : Clock Pulse
Rising Edge(positive-edge transition)
Falling Edge(negative-edge transition)

Setup time(20ns)

ts

th

minimum time that D input must remain at constant value before the
transition.

Hold time(5ns)
minimum time that D input must not change after the positive transition.

Propagation delay(max 50ns)
time between the clock input and the response in Q
일반 논리 gate에서는 2-20 ns이며 setup 및 hold time은 F/F에서만 정의되며
일반 논리 gate에서는 정의되지 않음.

Master-Slave F/F
2개의 F/F을 사용(Slave 와 Master F/F)하며 negative-edge transition 사용
위와 같이 사용하는 이유: Race 현상을 방지

Computer System Architecture

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-26

Race 현상
조건 - Hold time > Propagation delay
증상 - 0 과 1을 반복하다가 Unstable한 상태가 된다
해결책 - Edge triggered F/F (with little or no hold time) 또는 Master/Slave
F/F 사용
예제 : 7470(J-K Edge triggered F/F), 7471(J-K Master/Slave F/F)

Excitation Table
Required input combinations for a given change of state
Present State 와 Next State로 표현
SR F/F
Q(t) Q(t+1)
S
0
0
0
0
1
1
1
0
0
1
1
X

Don’t Care

Computer System Architecture

R
X
0
1
0

JK F/F
Q(t) Q(t+1)
J
0
0
0
0
1
1
1
0
X
1
1
X

0 : Set to 1
1 : Complement

K
X
X
1
0

D F/F
Q(t) Q(t+1)
0
0
0
1
1
0
1
1

D
0
1
0
1

T F/F
Q(t) Q(t+1)
0
0
0
1
1
0
1
1

T
0
1
1
0

1 : Clear to 0
0 : No change

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-27

1-7 Sequential Circuits
A sequential circuit is an interconnection of F/F and Gate
Clocked synchronous sequential circuit
Combinational Circuit = Gate
Sequential Circuit = Gate + F/F

Input

Combinational
Circuit

Output
Flip-Flops

Clock

Flip-Flop Input Equation
Boolean expression for F/F input
Input Equation 예제

x

DA

D

SET

CLR

Q

A

Q

A’

Q

B

Q

B’

DA = Ax + Bx, DB = A’x

Output Equation
DB

y = Ax’ + Bx’

Fig. 1-25 Example of a sequential
circuit

D

SET

Clock
CLR

y

Computer System Architecture

Chap. 1 Digital Logic Circuits

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-28

State Table

State Diagram
Graphical representation of state
table
Circle(state), Line(transition),
I/O(input/output)

Present state, input, next state, output 표현
Input Equ. = Next State
Present State

A
0
0
0
0
1
1
1
1

B
0
0
1
1
0
0
1
1

Input
x
0
1
0
1
0
1
0
1

Input Equ.

Ax
0
0
0
0
0
1
0
1

Bx
0
0
0
1
0
0
0
1

DA
0
0
0
1
0
1
0
1

Next State

DB
0
1
0
1
0
0
0
0

A
0
0
0
1
0
1
0
1

B
0
1
0
1
0
0
0
0

Output

y
0
0
1
0
1
0
1
0

0/0
00

Design Example: Binary Counter
x=0 0/00

x=1: 00, 01, 10, 11,
00, 01, …..
x=0: no change
State Diagram:
4 state(00, 01, 10, 11)

x=0

00

11

x=1 1/01

01

0/1 1/0

01

0/1
0/1

1/0

10

1/0

11

Excitation Table(2 bit counter = 2 F/F)
x=1

x=1

K
X
X
1
0

Next State =
Output

Present State

x=0
Computer System Architecture

x=1

JK F/F
Q(t) Q(t+1)
J
0
0
0
0
1
1
1
0
X
1
1
X

1/0

10
x=0

A
0
0
0
0
1
1
1
1

B
0
0
1
1
0
0
1
1

Input
x
0
1
0
1
0
1
0
1

Chap. 1 Digital Logic Circuits

Next State u
F/F Input
KA
A
B
JA
0
0
0
x
0
1
0
x
0
1
0
x
1
0
1
x
1
0
x
0
1
1
x
0
1
1
x
0
0
0
x
1

JB
0
1
x
x
0
1
x
x

KB
x
x
0
1
x
x
0
1

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.
1-29

Map for simplification

Logic Diagram

Input variable: A, B, x
B

B

JA
A

0

X

1

4

5

X

3

1
X

2

7

6

KA

X

A

x

X

0

X

4

1
5

X
1

3
7

4

A

K

6

CLR

Q

B

B

A

Q

2

KA=Bx

JA=Bx
0

SET

x

x

JB

X

J

1

3

2

1 X X
5
7
6
1 X X

KB
A

0

X X 1
4
5
X X 1

3

2

7

6

x

x

JB=x

1

KA=x

Sequential Circuit Design Procedure
1-5 절 참고(Combinational Circuit Design)
Sequential Circuit은 절차 3에서 State
diagram및 State table 이용
# of rows : 2m+n (m - State 수, n - Input 수)
Computer System Architecture

J

Chap. 1 Digital Logic Circuits

K

SET

CLR

Q

B

Q

Clock
1. The Problem is stated
2. I/O variables are assigned
3. Truth table(I/O relation)
4. Simplified Boolean Function
5. Logic circuit diagram

© Korea Univ. of Tech. & Edu.
Dept. of Info. & Comm.

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Computer organiztion1

  • 1. 1-1 Computer System Architecture M. Morris Mano 정보통신공학과 이 명 의(A-405) melee@kut.ac.kr Computer System Architecture Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 2. 1-2 Class Overview Contents Chap. 1 Digital Logic Circuits The fundamental knowledge needed for the design of digital systems constructed with individual gates and flip-flops. Chap. 2 Digital Components The logical operation of the most common standard digital components(Decoders, Multiplexers, Registers, Counters, and Memories). These digital components are used as building blocks for the design of larger units(Mano Machine). Chap. 3 Data Representation Various data types found in digital computers are represented in binary form in computer registers. Chap. 4 Register Transfer and Microoperations A register transfer language is used to express microoperations in symbolic form. Symbols are defined for arithmetic, logic, and shift microoperations. To show the hardware design of the most common microoperations, a composite arithmetic logic shift unit is developed. Chap. 5 Basic Computer Organization and Design The organization and design of a basic digital computer(Mano Machine). Register transfer language is used to describe the internal operation of the computer. By going through the detailed steps of the design presented in this chapter, the student will be able to understand the inner workings of digital computers. Computer System Architecture Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 3. 1-3 Class Overview Chap. 6 Programming the Basic Computer The 25 instructions of the basic computer to illustrate techniques used in assembly language programming. Programming examples are presented for a number of data processing tasks. The basic operations of an assembler are presented to show the translation from symbolic code to an equivalent binary program. Chap. 7 Microprogrammed Control Introduction to the concept of microprogramming. A specific microprogrammed control unit is developed to show by example how to write microcode for a typical set of instructions. The design of the control unit is carried-out in detail. Chap. 8 Central Processing Unit CPU as seen by the user(ISA). General register organization, the operation of memory stack, variety of addressing modes, instruction format. The Reduced Instruction Set Computer(RISC) concept. Chap. 9 Pipeline and Vector Processing The concept of pipelining is explained(Pipeline can speed-up processing). Both arithmetic and instruction pipeline is considered Vector processing is introduced(Example: Floating-point operations using pipeline procedures) Computer System Architecture Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 4. 1-4 Class Overview Chap. 10 Computer Arithmetic Arithmetic algorithms for digital hardware implementation(addition, subtraction, multiplication, and division). Chap. 11 Input-Output Organization Computer communication with input and output devices. I/O interface units are presented to show the way that the processor interacts with external peripherals. 4 modes of transfer : Programmed I/O, Interrupt initiated transfer, direct memory access, and IOP. Chap. 12 Memory Organization The concept of memory hierarchy : cache memory, main memory, auxiliary memory The organization and operation of associative memories is explained in detail. Memory Management Unit : physical address and logical address mapping Chap. 13 Multiprocessors A multiprocessor system is an interconnection of two or more CPUs. Various interconnection structures are presented : Time-shared common bus, Multiport Memory, Crossbar Switch, Multistage Switching Network, Hypercube Interconnection Interprocessor Arbitration : System bus, Serial Arbitration Procedure, Parallel Arbitration Logic, Dynamic arbitration Algorithms. Interprocessor Communication and Synchronization : Mutual Exclusion with a Semaphore Cache coherence Computer System Architecture Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 5. 1-5 Class Overview All 3 subjects associated with computer hardware in this book Computer Organization(Chap 1, 2, 3, 4) H/W components operation/connection. Various digital components used in the organization and design of digital computer. Computer Design(Chap 5, 6, 7) H/W Design/Implementation. The steps that a designer must go through to design and program an elementary digital computer(Chap. 6 : program = ISA) Computer Architecture(Chap 6, 8, 9, 11, 12) Structure and behavior of the computer as seen by the user » Information format, Instruction set, memory addressing : S/W = ISA » CPU, I/O, Memory : H/W Chapter in detail » » » » Computer System Architecture Chap. 6 : ISA Chap. 8 and 9 : CPU Chap. 11 : I/O Chap. 12 : Memory Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 6. 1-6 Class Overview What is “Computer Architecture”? - Hennessy and Patterson, Computer Organization and Design(1990) Computer Architecture Instruction Set Architecture (ISA) : S/W Machine Organization : H/W and Design “ISA(Instruction Set Architecture)”? the attributes of a system as seen by the programmer, i.e., the conceptual structure and functional behavior, as distinct from the organization of the data flows and controls, the logic design, and the physical implementation. - Amdahl, Blaaw, and Brooks(1964) Instructions, Addressing modes, Instruction and data formats, Register “Machine Organization”? CPU(Control & Data path), Memory, Input/Output Computer System Architecture Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 7. Class Overview 1-7 First Course in Computer Hardware Learn how a computer actually works Build the “Mano Machine” Learn one computer in detail, others are mastered easily. Homework: Solve the even number of problems Due at the beginning of the next class Optional “Mano Machine” Design Report Grade: Homework(20%) Optional Report(10%) Mid/Final Exam(each 30%) Class Participation(10%) Lecture Notes: http://microcom.kut.ac.kr Computer System Architecture Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 8. 8 Student Types 1-8 Insecure: 25 % Silent: 20 % Independent: 12 % Friendly: 11 % Obedient: 10 % Heroic: 9 % Critic: 9 % Unmotivated: 4 % - Michigan State University Computer System Architecture Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 9. 1-9 1-1 Digital Computers Digital Computer = H/W + S/W Digital implies that the information in the computer is represented by variables that take a limited number of discrete values. the decimal digits 0, 1, 2,….,9, provide 10 discrete values, but digital computers function more reliably if only two states are used. because of the physical restriction of components, and because human logic tends to be binary(true/false, yes/no), digital component are further constrained to take only two values and are said to be binary. Bit = binary digit : 0/1 Program(S/W) Application S/W API Operating System ROM BIOS A sequence of instruction S/W = Program + Data Computer H/W » The data that are manipulated by the program constitute the data base Application S/W = DB, word processor, Spread Sheet System S/W = OS, Firmware, Compiler, Device Driver Computer System Architecture Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 10. 1-10 1-1 Digital Computers continued Computer Hardware(H/W) CPU Memory Program Memory(ROM) Data Memory(RAM) Memory I/O Device Interface: 8251 SIO, 8255 PIO, 6845 CRTC, 8272 FDC, 8237 DMAC, 8279 KDI CPU Input Device: Keyboard, Mouse, Scanner Output Device: Printer, Plotter, Display Storage Device(I/O): FDD, HDD, MOD Input Device Interface or IOP Output Device Figure 1-1 Block Diagram of a digital Computer Computer System Architecture Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 11. 1-11 1-2 Logic Gates ADC(Analog to Digital Conversion) Signal Physical Quantity V, A, F, 거리 0 : 0.5v Binary Information Discrete Value 1 : 3v Gate The manipulation of binary information is done by logic circuit called “gate”. Blocks of H/W that produce signals of binary 1 or 0 when input logic requirements are satisfied. Digital Logic Gates : Fig. 1-2 AND, OR, INVERTER, BUFFER, NAND, NOR, XOR, XNOR x y Computer System Architecture xy x y xy Chap. 1 Digital Logic Circuits x x © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 12. 1-3 Boolean Algebra 1-12 Boolean Algebra Deals with binary variable (A, B, x, y: T/F or 1/0) + logic operation (AND, OR, NOT…) Boolean Function: variable + operation F(x, y, z) = x + y’z George Boole Born: 2 Nov 1815 in Lincoln, Lincolnshire, England Died: 8 Dec 1864 in Ballintemple, County Cork, Ireland Computer System Architecture Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 13. 1-13 1-3 Boolean Algebra Boolean Function: variable + operation F(x, y, z) = x + y’z Truth Table: Fig. 1-3(a) Logic Diagram: Fig. 1-3(b) Relationship between a function and variable Algebraic Expression Logic Diagram(gates로 표현) x y z 2n Combination Variable n = 3 Computer System Architecture F 0 0 0 0 1 1 1 1 0 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 x y F z Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 14. 1-14 Purpose of Boolean Algebra To facilitate the analysis and design of digital circuit Boolean function = Algebraic form = convenient tool Truth table (relationship between binary variables : Fig 1-3a) Algebraic form Logic diagram (input-output relationship : Fig. 1-3b) Algebraic form Find simpler circuits for the same function : by using Boolean algebra rules Boolean Algebra Rule : Tab. 1-1 - Operation with 0 and 1: x + 0 = x , x + 1 = 1 , x • 1 = x , x • 0 = 0 - Idempotent Law: x + x =x , x • x = x - Complementary Law: x + x' = 1 , x • x' = 0 - Commutative Law: x + y = y + x , x • y = y • x - Associative Law: x + (y + z) = (x + y) + z , x • ( y • z) = (x • y) • z - Distributive Law: x • ( y+ z) = (x • y) + (x • z) , x + (y • z) = (x + y) • (x + z) - DeMorgan's Law: (x + y)' = x' • y’ , (x • y )’ = x’ + y’ General Form: (x1 + x2 + x3 + … xn)' = x1' • x2' • x3' • … xn’ ( A U B ) c = Ac I B c (x1 • x2 • x3 • … xn) ' = x1' + x2' + x3' + … xn’ Computer System Architecture Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 15. 1-15 [예제] Fig. 1-6(a) [예제] F= AB’ + C’D + AB’ + C’D = x + x (let x= AB’ + C’D) =x = AB’ + C’D F= ABC + ABC’ + A’C = AB(C + C’) + A’C Fig. 1-6(b) = AB + A’C 1 inverter, 1 AND gate 감소 Fig. 1-4 2 graphic symbols for NOR gate x y z (x+y+z)’ x y z (a) OR-invert x’ y’z’ =(x+y+z)’ (b) invert-AND Fig. 1-5 2 graphic symbols for NAND gate x y z (xyz)’ (a) AND-invert Computer System Architecture x y z (x’+y’+z’) = (xyz)’ (b) invert-OR Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 16. 1-4 Map Simplification 1-16 Karnaugh Map(K-Map) Map method for simplifying Boolean expressions Minterm / Maxterm Minterm : n variables product ( x=1, x’=0) Maxterm : n variables sum (x=0, x’=1) 2 variables example x 0 y 0 Minterm x'y' m0 Maxterm x +y M0 0 1 x'y m1 x + y' M1 1 0 x y' m2 x'+ y M2 1 1 x y m3 x'+ y' M3 F = x’y + xy m1 M0 • M1 • M2 • M3 m3 = Σ(1,3) = Π (0,2) Computer System Architecture m0 + m1 + m2 + m3 ( m1 + m3 ) (Complement = M0 • M2 ) Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 17. 1-17 Map 3 variables 2 variables B 0 A C B 1 2 4 variables 3 0 3 5 7 0 6 A C 5 variables 1 3 2 4 2 4 A 1 5 7 6 12 13 15 14 8 C B 9 11 10 D 0 3 8 A 1 2 6 7 5 4 9 11 10 14 15 13 12 B 24 25 27 26 30 31 29 28 16 17 19 18 22 23 21 20 E Computer System Architecture D F Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 18. 1-18 [예제] F= x + y’z (2) F ( x , y , z ) = Σ(1,4,5,6,7 ) (1) Truth Table x 0 y 0 z 0 F 0 Minterm 0 0 1 1 m1 0 1 0 0 m2 0 1 1 0 m3 1 0 0 1 m4 1 0 1 1 m5 1 1 0 1 m6 1 1 1 1 m7 (3) Computer System Architecture y m0 0 x 1 3 2 4 5 7 6 z F= x + y’z Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 19. 1-19 Adjacent Square Number of square = 2n (2, 4, 8, ….) The squares at the extreme ends of the same horizontal row are to be considered adjacent 1 3 2 4 5 7 6 0 1 3 2 4 The same applies to the top and bottom squares of a column 0 5 7 6 12 13 15 14 8 9 11 10 Groups of combined adjacent squares may share one or more squares with one or more group Computer System Architecture Chap. 1 Digital Logic Circuits 0 0 1 3 4 5 7 0 1 3 5 7 5 7 6 13 15 14 9 11 10 2 4 2 12 6 3 4 2 1 8 The four corner squares of a map must be considered to be adjacent 6 © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 20. 1-20 B [예제] F ( A, B, C ) = Σ(3,4,6,7) 0 F=AC’ + BC A 3 2 4 5 7 6 0 A 1 3 2 4 5 7 6 C C [예제] F ( A, B, C , D ) = Σ(0,1,2,6,8,9,10) 0 Product-of-Sums Simplification F ( A, B, C , D ) = Σ(0,1,2,5,8,9,10) 3 2 5 7 6 12 13 15 14 8 A 1 4 F=B’D’ + B’C’ + A’CD’ F=B’D’ + B’C’ + A’C’D B C [예제] F ( A, B, C ) = Σ(0,2,4,5,6) F=C’ + AB’ 1 9 11 10 C D Sum of product 0 A Product of Sum Computer System Architecture Chap. 1 Digital Logic Circuits 1 3 2 4 F’=AB + CD + BD’(square marked 0’s) F’’(F)=(A’ + B’)(C’ + D’)(B’ + D) 전개 B 5 7 6 12 13 15 14 8 9 11 10 B D © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 21. 1-21 NAND Implementation Sum of Product : F=B’D’ + B’C’ + A’C’D B’ D’ C’ A’ D NOR Implementation Product of Sum : F=(A’ + B’)(C’ + D’)(B’ + D) A’ B’ C’ D’ D’ B Don’t care conditions 0 F(A,B,C)=Σ(0, 2, 6), d(A,B,C)= Σ(1, 3, 5) F=A’ + BC’= Σ(0, 1, 2, 3, 6) Computer System Architecture Chap. 1 Digital Logic Circuits A 4 X X 1 5 X 3 2 7 6 C © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 22. 1-22 1-5 Combinational Circuits Combinational Circuits in Combinational Circuits (Logic Gates) ... i0 i1 ... A connected arrangement of logic gates with a set of inputs and outputs Fig. 1-15 Block diagram of a combinational circuit f0 f1 fm Analysis Logic circuits diagram Design(Analysis의 반대) Boolean function or Truth table Experience 1. The Problem is stated 2. I/O variables are assigned 3. Truth table(I/O relation) 4. Simplified Boolean Function(Map 과 Boolean 대수 이용) 5. Logic circuit diagram Computer System Architecture Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 23. 1-23 Design Example : Full Adder 1. Full adder is a combinational circuits that forms the arithmetic sum of three input bit (Carry considered) 2. 3 Input(x, y, z), 2 Output(S: sum, C: carry) 3. Truth Table 4. Simplification x 0 0 0 0 1 1 1 1 Input y 0 0 1 1 0 0 1 1 z 0 1 0 1 0 1 0 1 Output C S 0 0 0 1 0 1 1 0 0 1 1 0 1 0 1 1 y y 0 3 5 7 6 z C= xy’z + x’yz + xy =z(xy’ + x’y) + xy =z(x ⊕ y) + xy 5. Logic circuit diagram x y c z s Computer System Architecture 0 2 4 x 1 Chap. 1 Digital Logic Circuits x 1 3 2 4 5 7 6 z S=xy’z’ + x’y’z + xyz + x’yz’ = z’(xy’ + x’y) + z(x’y’ + xy) = z’(x ⊕ y) + z(x ⊕ y)’ =a’b + ab’ (let a=z, b=x ⊕ y) =x ⊕ y ⊕ z (x ⊕y)’=(xy’+x’y)’ =(x’+y)(x+y’) =x’x+x’y’+xy+yy’ =x’y’+xy © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 24. 1-24 1-6 Flip-Flops Combinational Circuit = Gate Sequential Circuit = Gate + F/F Flip-Flop The storage elements employed in clocked sequential circuit A binary cell capable of storing one bit of information D(Data) F/F SR(Set/Reset) F/F S R SET CLR Q Q S 0 0 1 1 R 0 1 0 1 Q(t) 0 1 ? Q(t+1) no change clear to 0 set to 1 Indeterminate J K CLR Q Q J 0 0 1 1 K 0 1 0 1 CLR Q D 0 1 Q 0 1 Q(t+1) clear to 0 set to 1 “no change” condition이 없다 : Q(t+1)=D T(Toggle) F/F Q(t+1) Q(t) no change 0 clear to 0 1 set to 1 Q(t)' Complement JK F/F is a refinement of the SR F/F The indeterminate condition of the SR type is defined in complement Computer System Architecture SET 해결방법 : 1) Disable Clock 2) Feedback output into input p.52 JK(Jack/King) F/F SET D T SET CLR Q T 0 1 Q(t+1) Q(t) no change Q'(t) Complement Q T=1(J=K=1), T=0(J=K=0) 이면 JK F/F 수식 표현 : Q(t+1)= Q(t) ⊕ T xor Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 25. 1-25 Positive clock transition Edge-Triggered F/F State Change : Clock Pulse Rising Edge(positive-edge transition) Falling Edge(negative-edge transition) Setup time(20ns) ts th minimum time that D input must remain at constant value before the transition. Hold time(5ns) minimum time that D input must not change after the positive transition. Propagation delay(max 50ns) time between the clock input and the response in Q 일반 논리 gate에서는 2-20 ns이며 setup 및 hold time은 F/F에서만 정의되며 일반 논리 gate에서는 정의되지 않음. Master-Slave F/F 2개의 F/F을 사용(Slave 와 Master F/F)하며 negative-edge transition 사용 위와 같이 사용하는 이유: Race 현상을 방지 Computer System Architecture Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 26. 1-26 Race 현상 조건 - Hold time > Propagation delay 증상 - 0 과 1을 반복하다가 Unstable한 상태가 된다 해결책 - Edge triggered F/F (with little or no hold time) 또는 Master/Slave F/F 사용 예제 : 7470(J-K Edge triggered F/F), 7471(J-K Master/Slave F/F) Excitation Table Required input combinations for a given change of state Present State 와 Next State로 표현 SR F/F Q(t) Q(t+1) S 0 0 0 0 1 1 1 0 0 1 1 X Don’t Care Computer System Architecture R X 0 1 0 JK F/F Q(t) Q(t+1) J 0 0 0 0 1 1 1 0 X 1 1 X 0 : Set to 1 1 : Complement K X X 1 0 D F/F Q(t) Q(t+1) 0 0 0 1 1 0 1 1 D 0 1 0 1 T F/F Q(t) Q(t+1) 0 0 0 1 1 0 1 1 T 0 1 1 0 1 : Clear to 0 0 : No change Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 27. 1-27 1-7 Sequential Circuits A sequential circuit is an interconnection of F/F and Gate Clocked synchronous sequential circuit Combinational Circuit = Gate Sequential Circuit = Gate + F/F Input Combinational Circuit Output Flip-Flops Clock Flip-Flop Input Equation Boolean expression for F/F input Input Equation 예제 x DA D SET CLR Q A Q A’ Q B Q B’ DA = Ax + Bx, DB = A’x Output Equation DB y = Ax’ + Bx’ Fig. 1-25 Example of a sequential circuit D SET Clock CLR y Computer System Architecture Chap. 1 Digital Logic Circuits © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 28. 1-28 State Table State Diagram Graphical representation of state table Circle(state), Line(transition), I/O(input/output) Present state, input, next state, output 표현 Input Equ. = Next State Present State A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 Input x 0 1 0 1 0 1 0 1 Input Equ. Ax 0 0 0 0 0 1 0 1 Bx 0 0 0 1 0 0 0 1 DA 0 0 0 1 0 1 0 1 Next State DB 0 1 0 1 0 0 0 0 A 0 0 0 1 0 1 0 1 B 0 1 0 1 0 0 0 0 Output y 0 0 1 0 1 0 1 0 0/0 00 Design Example: Binary Counter x=0 0/00 x=1: 00, 01, 10, 11, 00, 01, ….. x=0: no change State Diagram: 4 state(00, 01, 10, 11) x=0 00 11 x=1 1/01 01 0/1 1/0 01 0/1 0/1 1/0 10 1/0 11 Excitation Table(2 bit counter = 2 F/F) x=1 x=1 K X X 1 0 Next State = Output Present State x=0 Computer System Architecture x=1 JK F/F Q(t) Q(t+1) J 0 0 0 0 1 1 1 0 X 1 1 X 1/0 10 x=0 A 0 0 0 0 1 1 1 1 B 0 0 1 1 0 0 1 1 Input x 0 1 0 1 0 1 0 1 Chap. 1 Digital Logic Circuits Next State u F/F Input KA A B JA 0 0 0 x 0 1 0 x 0 1 0 x 1 0 1 x 1 0 x 0 1 1 x 0 1 1 x 0 0 0 x 1 JB 0 1 x x 0 1 x x KB x x 0 1 x x 0 1 © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.
  • 29. 1-29 Map for simplification Logic Diagram Input variable: A, B, x B B JA A 0 X 1 4 5 X 3 1 X 2 7 6 KA X A x X 0 X 4 1 5 X 1 3 7 4 A K 6 CLR Q B B A Q 2 KA=Bx JA=Bx 0 SET x x JB X J 1 3 2 1 X X 5 7 6 1 X X KB A 0 X X 1 4 5 X X 1 3 2 7 6 x x JB=x 1 KA=x Sequential Circuit Design Procedure 1-5 절 참고(Combinational Circuit Design) Sequential Circuit은 절차 3에서 State diagram및 State table 이용 # of rows : 2m+n (m - State 수, n - Input 수) Computer System Architecture J Chap. 1 Digital Logic Circuits K SET CLR Q B Q Clock 1. The Problem is stated 2. I/O variables are assigned 3. Truth table(I/O relation) 4. Simplified Boolean Function 5. Logic circuit diagram © Korea Univ. of Tech. & Edu. Dept. of Info. & Comm.