Page 52 - Digital Electronics by harish

Example 2 : (54) 10 - (62) 10

Binary of 54 (Minuend) = 110110
Binary of 62 (Subtrahend) = 111110

2‟s complement of 111110 = 000010

Minuend 110110
Add 2‟s complement of Subtrahend + 000010
111000 There is no carry.
Find 2‟s complement 000111
(1‟s complement Plus 1) + 1
- 001000 Result is negative.
Convert to Decimal - 8

Answer : - 8

Signed binary numbers

In decimal systems, we use (+) sign for positive numbers and (–) sign for negative numbers.
In binary number system, an additional bit is used as the sign bit. A „0‟ is used to represent a
positive number and a „1‟ is used to represent a negative number.

Sign
bit Magnitude bits

For example, an 8-bit signed number 01000100 represents a positive number, because the
sign bit is „0‟. Its magnitude is 1000100. Hence, the equivalent decimal number is +68.
Similarly, the signed number 11000100 represents a negative number, because the sign bit is
„1‟. Its magnitude is 1000100. Hence, the equivalent decimal number is -68.

ie. 01000100 = +68
11000100 = -68

This type of representation for signed numbers is called „sign-and-magnitude representation‟.

2.2 Half adder

Half adder adds two binary digits at a time. It has two inputs A and B, and two outputs SUM
and CARRY.

Figure : Block diagram

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