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Binary numbers addition is straight forward process while binary subtractions involve three fundamentals. Discuss those in details with formula and examples.

Binary Subtraction:

Suppose,   M is Minuend and  N is subtrahend

Then, M – N can be done based on three steps discussed next:

Step 1: Take 2’s complement of N and add it to M.

M – N = M + (2^n – N)

Step 2: If M is greater than or equal to N then end carry is discarded from the result.

M –N = M + (2^n – N) – 2^n

Step 3: If M is less than N then take 2’s complement of the result and append negative ‘-‘ sign in front

So binary subtraction formula , M-N = (-) [2^n – (M + (2^n -1))]. .

Example 1 : Perform binary subtraction of two binary numbers M = 10101010 and N = 00111000

Example 2 : Perform binary subtraction of two binary numbers N = 10101010 and M = 00111000

Binary subtraction Discussion

M – N

Discard end carry from the subtraction

Answer. Binary subtraction of M and N = 01110010

    10101010                                             10101010

-   00111000                                           +11001000

M – N

    00111000                                                   00111000

-   10101010                                                + 01010110

                                                  Result     =    10001110

No end carry in result

2’s complement of result = 01110010

Answer. Binary subtraction of M and N = - (2’s complement of result) = -01110010 

                                                               1 01110010

End carry

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