# Decimal-to-Binary Conversion

To convert decimal number into binary form,  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,  successively multiply the fractional part of the decimal number by 2 and record the carry until the result of multiplication is ‘0’. The carry sequence written in forward order forms 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.

e. g.

Find 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