# Use a Karnaugh’s map to design if the output bit is 0 if the first and fourth input are same else it is 1 for 4 input bits – IGNOU MCA Assignment 2015 – 16

By | August 31, 2015

MASTER OF COMPUTER APPLICATIONS

Course Code : MCS-012
Course Title : Computer Organisation and Assembly Language Programming
Assignment Number : MCA(I)/012/Assignment/15-16
Maximum Marks : 100
Weightage : 25%

Use a Karnaugh’s map to design a circuit that takes four input bits and produces one output bit. The output bit is 0 if the first and fourth input are same else it is 1.

Before Designing we should know inputs which is 4

That means 24 = 16 Combinations of outputs

Inputs are represented as ABCD

Output is represented by F and some times termed as Function

 Decimal A B C D F (Function) 0 0 0 0 0 1 0 0 0 1 2 0 0 1 0 3 0 0 1 1 4 0 1 0 0 5 0 1 0 1 6 0 1 1 0 7 0 1 1 1 8 1 0 0 0 9 1 0 0 1 10 1 0 1 0 11 1 0 1 1 12 1 1 0 0 13 1 1 0 1 14 1 1 1 0 15 1 1 1 1

Before proceeding we should know what odd parity is for ABCD inputs?

There are two types of parity even parity and odd parity

The parity is 0 or 1 depending upon total numbers of 1s

If count of 1s is even number then even parity = 0 and odd parity = 1

Similarly If count of 1s is odd number then even parity = 1 and odd parity = 0

After Finding out odd parity for ABCD inputs

We have Table as:-

 Decimal A B C D F (Function) 0 0 0 0 0 0 1 0 0 0 1 1 2 0 0 1 0 0 3 0 0 1 1 1 4 0 1 0 0 0 5 0 1 0 1 1 6 0 1 1 0 0 7 0 1 1 1 1 8 1 0 0 0 1 9 1 0 0 1 0 10 1 0 1 0 1 11 1 0 1 1 0 12 1 1 0 0 1 13 1 1 0 1 0 14 1 1 1 0 1 15 1 1 1 1 0

It’s can also be written as F =Σ (1, 3, 5, 7, 8, 10, 12, 14)

Only the decimal number where we find 1’s is shown in the Bracket.

Final Equation:-