1. Foundation of Computer Science
Junior Programmer Camp #8

2. Chapter 1: Number Systems & Radix Number

3. Radix Numbers
• Base 2 (Binary)
- 0, 1
• Base 8 (Octal)
- 0, 1, 2, 3, 4, 5, 6, 7
• Base 10 (Decimal)
- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• Base 16 (Hexadecimal)
– 0, 1, 2, 3 , …, 8, 9, A, B, C, D, E, F

4. Base Conversion
Base X to Base 10 (Decimal)
– Starting from the last digit, multiply
that digit by X0
– Increase the power of X by 1 and
repeat until you have done all digits
– Sum up the results

5. Base Conversion (cont.)
Example:
Convert 110112, 5467, 878 to base 10
Result :
27
279
71

6. Base Conversion (cont.)
Base 10 (Decimal) to any base X
– Divide the number by X.
– Write down the remainder.
– Repeat the previous two steps until
the result is 0.
– The actual result is the digit sequence
of the remainders from the last to first.

7. Base Conversion (cont.)
Example:
Convert 34510 to base 2,3,16
Result:
1010110012
11021203
15916

8. Base Conversion (cont.)
Base 2 (Binary) to Base 8 (Octal)
– Group 3 digits from the right side
– Convert each group to its octal
representation
Do you think that number in base 2 can
also be converted to Base 16
(Hexadecimal) directly somehow?

9. Binary Arithmetic
• Addition:
0+0=0
1+0=1
0+1=1
1 + 1 = 10
• Subtraction:
0–0=0 1–0=1
0–1=1
1-1=0
• Multiplication:
0x0=0 1x0=0
0x1=0
1x1=1

10. Binary Arithmetic (Try it!)
Example:
101001101 + 111110101
1001001011 - 11011101
11101 x 11001

11. Chapter 2: Logic Gates & Circuits

12. Gates and Circuits Simulator
http://logic.ly/demo/

13. NOT Gate
Boolean expression : A’
Truth table:
Input
Output
0
1
1
0

14. AND & NAND Gate
Boolean expression : A ∙ B
[AND]
(A ∙ B)’ [NAND]
Truth table:
Input
Output
A
B
AND
NAND
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0

15. OR & NOR Gate
Boolean expression : A + B
[OR]
(A + B)’ [NOR]
Truth table:
Input
Output
A
B
OR
NOR
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0

16. XOR & XNOR Gate
Boolean expression : A B
[XOR]
(A B)’ [XNOR]
Truth table:
Input
Output
A
B
XOR
XNOR
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1

17. Circuits
A circuit is a combination of gates.

18. Boolean expression
Boolean expression is
D = (A + B)’
E = B ∙ C
Q = D + E
= (A + B)’+(B ∙ C)
NOT (A OR B)
B AND C
D OR E
(NOT (A OR B)) OR (B AND C)

19. Truth table
Input
Output
A
B
C
D
(A + B)’
E
(B ∙ C )
Q
((A + B)’+(B ∙ C) )
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1

20. Give it a try!
Find the Boolean expression and
the truth table of this circuit.

21. Give it a try!
Draw a circuit this Boolean expression:
X = ((A
B) + (C’∙ D))’
E