AS we already know Binary number can be represented only by using 0’s and 1’s, but can not use the sign (-) to denote the negative number or sign (+) to denote the positive number. So it must be either 0 or 1. There are three methods to represent binary number. They are

- Sign and magnitude method
- One’s complement method
- Two’s complement method

**Sign and magnitude method**

In this method, first bit is considered as a sign bit. Here positive number starts with 0

and negative number starts with 1.

**Example**

25

25/2 = 12 1

12/2 = 6 0

6/2 = 3 0

3/2 = 1 1

1/2 = 0 1

So the binary number is (11001)2. If we take the size of the word is 1 byte, then the number 25 will be represented as

00011001 Suppose, if the number is -25, and then it will be represented as 10011001

**One’s Complement Method**

In this method, the positive number is represented as same as the binary number. If the number is negative, then we need to find one’s complement of a binary number. The one’s complement of a binary number will replace every 0 with 1 and vice- versa.

**Example**

(i) Represent 86 in one’s complement method (I byte representation)

86/2 =43 0

43/2 =21 1

21/2 =10 1

10/2 =5 0

5/2 =2 1

2/2 =1 0

1/2 =0 1

The binary number is 1010110 1 byte representation of number 86 is 01010110

**Two’s Complement method**

In this method, the positive number is represented as the binary number. If the number is negative, then we need to calculate two’s complement of a binary number. The two’s complement of a binary number is calculated by adding 1 to its one’s complement.

**Example**

(i) Represent 87 in two’s complement method (I byte representation)

87/2 =43 1

43/2 =21 1

21/2 =10 1

10/2 =5 0

5/2 =2 1

2/2 =1 0

1/2 =0 1

The binary number is 1010111

Hence, the 1 byte representation of number 86 is 01010111

(ii) Represent -54 two’s complement method (I byte representation)

54/2 =27 0

27/2 =13 1

13/2 =6 1

6/2 =3 0

3/2 =1 1

1/2 =0 1

The binary number is 110110

Hence, the 1 byte representation is 00110110

The given number is negative; hence we need to calculate two’s complement.

One’s complement of 00110110 is 11001001 (convert 1 into 0 and 0 into 1)

add 1 to one’s complement

1

11001001 (1+1=2, binary equivalent =11)

+ 1

———————-

11001010

Thus, 1 byte representation of number -54 is 11001010

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