Page 9 - Digital Electronics by harish

1.1.2 Conversion

Decimal to binary conversion

i) Integer numbers

The “double dabble” method is used to convert decimal number to binary number. In
this method, the decimal number is divided by 2 repeatedly and the remainders are noted after
each division. We have to continue until we get zero in the quotient. The remainders are
taken from bottom to top to get the binary number.

Example: To convert the decimal number 27 to binary number

27 † 2 = 13 → Remainder 1
13 † 2 = 6 → Remainder 1
6 † 2 = 3 → Remainder 0
3 † 2 = 1 → Remainder 1
1 † 2 = 0 → Remainder 1

Therefore, 27 10 = 11011 2

ii) Fractional numbers

The decimal number is multiplied by 2 repeatedly and the carries integer part (whole
numbers) is noted after each multiplication. We have to continue until we get zero in the
fraction. The process may be stopped after six places. The carries are taken from top to
bottom to get the binary number.

Example: To convert the decimal number 0.85 to binary number.

0.85 x 2 = 1.7 = 0.7 with carry → 1
0.7 x 2 = 1.4 = 0.4 with carry → 1
0.4 x 2 = 0.8 = 0.8 with carry → 0
0.8 x 2 = 1.6 = 0.6 with carry → 1
0.6 x 2 = 1.2 = 0.2 with carry → 1
0.2 x 2 = 0.4 = 0.4 with carry → 0

Therefore, 0.85 10 = 0.110110 2

Decimal to octal conversion

i) Integer numbers

The “octal dabble” method is used to convert decimal number to octal number. In this
method, the decimal number is divided by 8 repeatedly and the remainders are noted after
each division. We have to continue until we get zero in the quotient. The remainders are
taken from bottom to top to get the octal number.

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