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:-

Kmap012