Binary subtraction is performed using one’s complement and 2’s complement methods

**1’s complement Subtraction method**

Step 1: Find the ones complement of the subtrahend

Step 2: Add the subtractor and ones complement of the subtrahend

Step 3: If carry is present add the carry to the result

Step 4: If carry is not obtained the number is in its negative ones complement form

**Example 25:** find 12-3 using ones complement method

Ones complement of subtrahend 3 = 1100.

12 – 3 =+9 → 1100_{2}+0011_{2}=1001_{2}

**Example 26:** find 12-15 using ones complement method

Ones complement of subtrahend 15 = 0000

Taking the ones complement of the result 1100 → (-)0011

## 2’s complement subtraction

Step 1: Find the two’s complement of the subtrahend

Step 2: Add the subtractor and two’s complement of the subtrahend

Step 3: If carry is present Discard the carry

Step 4: If carry is not obtained the number is in its negative two’s complement form

**Example:** find 14-3 using 2’s complement method

The binary value of subtrahend 3 = 0011

1’s complement of subtrahend 3 = 1100

2’s complement of subtrahend 3 =1101

14 – 3 =+11 → 1110_{2 }– 0011_{2}=1011_{2}

**Example:** find 3-14 using ones complement method

The binary value of subtrahend 14 = 1110

1’s complement of subtrahend 14 = 0001

2’s complement of subtrahend 3 =0010

Taking the ones complement of the result 0101_{2} → (-) 1011_{2} (-11)_{10}

## Subtraction using 9’s complement

Subtraction using 9’s complement uses the same principles as that of the binary complement subtraction

**Example :** subtract using 9’s complement of the following decimal numbers 66-44

9’s complement of 44 =99-44=55

66_{10} – 4_{10} = 22_{10}

## Subtraction using 10’s complement

Subtraction using 10’s complement uses the same principles as that of the 9’s complement subtraction. Find the 9s complement add 1 to the 9’s complement and add the numbers, discard the carry to obtain the final results.

**Example:** subtract using 10’s complement of the following decimal numbers 66-44

9’s complement of 44 =99-44=55

10’s complement of 44=55+1=56

66_{10} – 4_{10} = 22_{10}