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 → 11002+00112=10012
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 → 11102 – 00112=10112
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 01012 → (-) 10112 (-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
6610 – 410 = 2210
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
6610 – 410 = 2210
