The document discusses converting decimal numbers to binary numbers. It explains that the integer and fractional parts of a decimal number are dealt with separately. To convert the integer part, the number is repeatedly divided by 2 and the remainders are written down and taken in reverse order to form the binary number. To convert the fractional part, the number is repeatedly multiplied by 2 and the integer parts are taken in forward order. Examples are provided of converting the decimal numbers 125, 0.4375, and 17.35 to their equivalent binary numbers.

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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