1. Conversions of decimal to binary number
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2. Objective
On completion of this period, you would be
able to know:
Conversion of a decimal number to
equivalent binary
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3. Recap
Various number systems used in
digital computer
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4. Conversions from one
Number System to other
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5. Conversion from decimal to binary
The integer and fractional parts of the decimal
number are dealt separately.
 The decimal number is divided by 2
successively.
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6. Conversion of decimal to binary
 The quotient and remainder are noted down at
each stage.
 The present quotient is again divided by 2 and
repeat the above step.
 This process is repeated until the quotient
becomes 0.
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7. Conversion from decimal to binary
Integer part:
 Divide the integer part of the given decimal
number repeatedly by 2.
 And write down the remainder after each division.
 The remainders are then taken in reverse order
(bottom to top) to form binary equivalent to the
number
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8. Fractional part:
 The fractional part of the given decimal
number is multiplied repeatedly by 2, each
time recording the carry (integer part).
 The integers are then taken in forward order
(top to bottom) to form the binary equivalent of
the number.
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9. Fractional part (contd) :
 This process is continued until the fraction
becomes zero
(or)
until sufficient accuracy is obtained.
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10. Convert the decimal number 125 to binary.
division
125 remainder
2 62 1
2 23 0
2 15 1
2 7 1
2 3 1
2 1 1
0 1
Thus (125)10 = (1111101)2
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11. Convert the decimal number 0.4375 to
binary.
Multiplication Product Integral part
0.4375*2 0.8750 0
0.8750*2 1.75 1
0.75*2 1.50 1
0.5*2 1.00 1
Taking the integers parts in the forward (top to
bottom) gives the binary fraction 0.0111.
Thus (0.4375)10= (0.0111)2
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12. Convert the decimal number 17.35 to binary.
Division Remainders
2 17
2 8 1
2 4 0
2 2 0
2 1 0
2 0 1
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13. Fractional part:
Multiplication Product Integral part
0.35*2 0.70 0
0.70*2 1.40 1
0.40*2 0.80 0
0.80*2 1.60 1
0.60*2 1.20 1
0.20*2 0.40 0
Thus (17.35)10= (10001.010110.......)2
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14. Summary
In this class, we have learnt about
Conversion from decimal numbering
system to binary numbering system
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15. Frequently Asked Questions
1. Explain the procedure to convert a decimal
number into binary number?
2. Convert the decimal real number 12.625 8 into
equivalent binary real number?
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16. Quiz:
1. The base of binary system is
a. 10
b. 2
c. 8
d. 16
Answer: b
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17. Quiz:
2. What is the binary equivalent of 10
a. 1000
b. 1011
c. 1010
d. 1111
Answer: c
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18. Quiz:
3. What is the binary equivalent of 125
a. 1111101
b. 1111001
c. 1101101
d. 1111111
Answer: a
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