Adder and Substractor

Here the output ‘1’of ‘10’ becomes the carry-out. The result is shown in a truth-table below. ‘SUM’ is the normal output and ‘CARRY’ is the carry-out.From the equation it is clear that this 1-bit adder can be easily implemented with the help of EXOR Gate for the output ‘SUM’ and an AND Gate for the carry.

For complex addition, there may be cases when you have to add two 8-bit bytes together. This can be done only with the help of full-adder logic.

Full Adder :- This type of adder is a little more difficult to implement than a half-adder. The main difference between a half-adder and a full-adder is that the full-adder has three inputs and two outputs. The first two inputs are A and B and the third input is an input carry designated as CIN. The output carry is designated as COUT and the normal output is designated as S. Take a look at the truth-table.

 

From the above truth-table, the full adder logic can be implemented. We can see that the output S is an EXOR between the input A and the half-adder SUM output with B and CIN inputs. We must also note that the COUT will only be true if any of the two inputs out of the three are HIGH.

Subtractor : Subtractor is the one which used to subtract two binary number(digit) and provides Difference and Borrow as a output.In digital electronics we have two types of subtractor. 1.Half Subtractor     2.Full Subtractor  

1. Half Subtractor :Half Subtractor is used for subtracting one single bit binary digit from another single bit binary digit.The truth table of Half Subtractor is shown below.

Logic Diagram

 

 

 

 

 

 

 

 

 

Like Adders Here also we need to calculate the equation of  Difference and Borrow

Difference = A'B+AB'=A B
Borrow=A'B

Full Subtractor : A logic Circuit Which is used for Subtracting Three Single bit Binary digit is known as Full Subtractor.The Truth Table of Full Subtractor is Shown Below.

LOGIC DIAGRAM

 

 

 

 From the Truth Table The Difference and Borrow will written as
Difference=A'B'C+A'BB'+AB'C'+ABC
Reduce it like adder
Then We got
Difference=A B C
Borrow=A'B'C+A'BC'+A'BC+ABC
=A'B'C+A'BC'+A'BC+A'BC+A'BC+ABC    ---------->  A'BC=A'BC+A'BC+A'BC
=A'C(B'+B)+A'B(C'+C)+BC(A'+A)
Borrow=A'C+A'B+BC