Page 49 - Digital Electronics by harish

2.1.3 Representation of negative numbers

In decimal systems, we use (+) sign for positive numbers and (–) sign for negative numbers.
But in binary numbers, complement method is used for representing negative numbers. Two
types of complement methods are available.

1) 1‟s complement method
2) 2‟s complement method

Either 1‟s complement or 2‟s complement method is adopted in a particular digital system.

1’s complement

1‟s complement is used to represent negative numbers. Each bit is subtracted from 1 (borrow
is ignored) to get the 1‟s complement. A shortcut method is also used. Each bit in the given
number is complemented (0 to 1, 1 to 0) to get its 1‟s complement.

Examples :

1) Find the 1‟s complement of 101011.

010100 ---- 0 to 1, 1 to 0

Answer :10100

2) Find the 1‟s complement of 11110.

00001 ---- 0 to 1, 1 to 0

Answer : 1

2’s complement

2‟s complement is used to represent negative numbers. When we add 1 to 1‟s complement,
we will get the 2‟s complement of the given number.

Examples :

1) Find the 2‟s complement of 101011.

1‟s complement 010100 ---- 0 to 1, 1 to 0
Add 1 + 000001
2‟s complement 010101

Answer : (010101) 2

2) Find the 2‟s complement of 11110.

1‟s complement 00001 ---- 0 to 1, 1 to 0
Add 1 + 00001
2‟s complement 00010

Answer :(00010) 2

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