Page 19 - computer science (868) class 11
P. 19
1.2.1 Decimal to Binary
Firstly, the integer part is converted into binary and then the fractional part is converted. The steps to be followed are:
1. For integer part, divide the number by 2 and store the remainder of the division separately.
2. Assign quotient as the new dividend.
3. Repeat steps 1 & 2 until new dividend = 0.
4. Arrange the remainders from bottom (LSB) to top (MSB) to get the result.
5. For decimal part, repeat step 6 until the fractional part becomes 0 or up to 4 places of decimal.
6. Multiply fractional part by 2 and store the integer part of the product separately.
7. Arrange the binary digits of the integer part from top to bottom for the result of the fractional part.
This method also called the Double-Dabble method involves successive division of the number by 2. We read data in
their usual representation as decimal numbers. Circuits built internally convert this decimal number into binary for
digital computation.
Let us understand with an example:
Example: Convert (77.45) to binary.
10
1. On dividing 77 by 2, we get 38 as quotient and 2 77
1 as remainder. 38 (quotient) 1 (First remainder)
2. Now, 38 is the new dividend. On dividing it by 2 38
2, we get 19 as quotient and 0 as remainder. 19 (quotient) 0 (Second remainder)
3. On dividing 19 by 2, we get 9 as quotient and 2 19
1 as remainder. 9 (quotient) 1 (Third remainder)
4. Dividing 9 by 2 gives 4 as quotient and 1 as 2 9
remainder. 4 (quotient) 1 (Fourth remainder)
5. Dividing 4 by 2 gives 2 as quotient and 0 as 2 4
remainder. 2 (quotient) 0 (Fifth remainder)
6. Dividing 2 by 2 gives 1 as quotient and 0 as 2 2
remainder. 1 (quotient) 0 (Sixth remainder)
7. Dividing 1 by 2 gives 0 as quotient and 1 2 1
as remainder. As quotient 0 is reached, the 0 (quotient) 1 (Seventh remainder)
remainders are read upwards.
8. Multiplying fractional part 0.45 by 2 gives 0.90.
Store integral part 0. 0.45 × 2 = 0.90 Integral part = 0
9. Multiplying fractional part 0.90 by 2 gives 1.80.
Integral part 1 is separated. 0.90 × 2 = 1.80 Integral part = 1
10. Multiplying fractional part 0.80 by 2 gives 1.60.
Keep 1 separately. 0.80 × 2 = 1.60 Integral part = 1
11. Multiplying fractional part 0.60 by 2 gives 1.20.
Keep 1 separately. The process will continue 0.60 × 2 = 1.20 Integral part = 1
infinitely. Thus, we will stop after four places
of decimal to take the approximate answer by
arranging from top to bottom. Corresponding
binary number will be (1001101.0111) .
2
17
Numbers 17

