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Digital Electronics
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
1 3
—
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
1.11 Decimal-to-Octal Conversion
The process of decimal-to-octal conversion is similar to that of decimal-to-binary conversion. The
progressive division in the case of the integer part and the progressive multiplication while working
on the fractional part here are by ‘8’ which is the radix of the octal number system. Again, the integer
and fractional parts of the decimal number are treated separately. The process can be best illustrated
with the help of an example.
Example 1.4
We will find the octal equivalent of (73.75) 10
Solution
• The integer part = 73
Divisor Dividend Remainder
8
7 3
—
8
9
1
8
1
1
—
0
1