Decimal to Binary Conversion

       As outlined earlier, the integer and fractional parts are worked on separately. For the integer part,
the binary equivalent can be found by successively dividing the integer part of the number by 2
and recording the remainders until the quotient becomes ‘0’. The remainders written in reverse order
constitute the binary equivalent. For the fractional part, it is found by successively multiplying the
fractional part of the decimal number by 2 and recording the carry until the result of multiplication
is ‘0’. The carry sequence written in forward order constitutes the binary equivalent of the fractional
part of the decimal number. If the result of multiplication does not seem to be heading towards zero in the
case of the fractional part, the process may be continued only until the requisite number of equivalent bits
has been obtained. This method of decimal–binary conversion is popularly known as the double-dabble
method. The process can be best illustrated with the help of an example.

Example 1.3
We will find the binary equivalent of (13.375)10.
Solution
• The integer part = 13
Divisor Dividend Remainder
2 13 —
2 6 1
2 3 0
2 1 1
— 0 1
• The binary equivalent of (13)10 is therefore (1101)2
• The fractional part = .375
• 0.375 × 2 = 0.75 with a carry of 0
• 0.75 × 2 = 0.5 with a carry of 1
• 0.5 × 2 = 0 with a carry of 1
• The binary equivalent of (0.375)10
= (.011)2
• Therefore, the binary equivalent of (13.375)10
= (1101.011)2