BINARY SUBTRACTION

Binary subtraction

   is simplified as well, as long as we remember how subtraction and the base 2 number system. Let's first look at an easy example.

  111

 - 10

  101

Note that the difference is the same if this was decimal subtraction. Also similar to decimal subtraction is the concept of "borrowing." Watch as "borrowing" occurs when a larger digit, say 8, is subtracted from a smaller digit, say 5, as shown below in decimal subtraction.

    35

  -   8

    27

For 10 minus 1, 1 is borrowed from the "tens" column for use in the "ones" column, leaving the "tens" column with only 2. The following examples show "borrowing" in binary subtraction.

    10       100      1010

   -  1       - 10     - 110

      1          10       100

BINARY SUBTRACTOR

HALF SUBTRACTOR

The half-subtractor is a combinational circuit which is used to perform subtraction of two bits. It has two inputs, A (minuend) and Y (subtrahend) and two outputs D (difference) and B (borrow).

It is an arithmetic circuit that subtracts one bit from the other. It is used to subtract the LSB of the subtrahend from the LSB of the minuend when a binary number is to be subtracted from the other. A logic circuit is called half adder which accepts two binary digits as its input and produces two binary digits on its output terminals known as difference bit and borrow bit. 

From the above table one can draw the karnaugh map for "difference" and "borrow".

So, Logic equations are:

From these two expression implementation requirement for a half subtractor function requires one Ex-OR gate for Difference generation and an AND gate with a NOT gate for Borrow generation.  

FULL SUBTRACTOR

A full subtractor is a combinational digital circuit that is used to carry out subtraction involving three bits. This circuitry is then used in a cascade arrangement to synthesize multiple bit subtractor circuits. There are three input and two output bits that are involved in an nth bit full subtractor circuit  

Logic equations are: