Digital Computer Electronics
PRESTON UNIVERSITY LAHORE CAMPUS
1-A Ahmed Block New Garden Town Lahore
Assignment-I: Digital Computer Electronics (DCE)
Semester: Fall-2012
Task: K-map Simplification
Student Name: Shaukat Mahmood (03007411855)
Registration No. 16D2-212022
Program: B-Tech Pass (Advance)
Quarter: 5th
Submitted to: Professor Assad Umer Khan
Assignment Task:
USE OF KARNAUGH MAP FOR SIMPLIFICATION OF LOGIC CIRCUIT/ EXPRESSION
Rules for Karnaugh Map Simplification:
Followings are the rules to use k-Map for logic circuit simplification 1. Enter a 1 on the Karnaugh map for each fundamental product term that corresponds to 1 output, in the truth table. Enter 0s elsewhere. 2. Encircle the octets, quads, and pairs. Remember to roll and overlap to get the largest groups possible. 3. If any isolated 1s remain, encircle them. 4. Eliminate redundant groups if any exist. 5. Indicate don’t condition, if any, with X instead of 1s or 0s. 6. Treat X as 0 or 1 to form octets, quads or pair, as per simplification requirement. 7. Write the Boolean equation by ORing the products corresponding to the encircled groups. 8. Draw the equivalent logic circuit.
Example-1: Simplify the following Boolean Equation using K-Map
Y= A’B’C’D+ A’B’CD’+ A’B’CD+ A’BC’D’+ A’BCD’+ AB’C’D’+ AB’C’D+ AB’CD’+ ABC’D’+ ABC’D+ ABCD’
Solution:
Now for
Group-I Group-II Group-IIi
ABCD ABCD ABCD
0001 1100 0010
0011 1101 0110 A’B’D 1000 1110 1001 1010 AC’ CD’
Simplified SOP is
Y=A’B’D+AC’+CD’
Example-2: Simplify the following Boolean Equation using K-Map
Y=A’BC’D’+ABC’D’+ABC’D+ABCD+ABCD’+AB’C’D’_AB’C’D+AB’CD+AB’CD’
Now for, Group-I Group-II
ABCD ABCD
0101 1100
1101 1101 BC’D 1111 1110 1000 1001 1011 1010 A
Simplified SOP equation is Y=A+BC’D
Example-3: Simplify the following Boolean Equation using K-Map
1-A Ahmed Block New Garden Town Lahore
Assignment-I: Digital Computer Electronics (DCE)
Semester: Fall-2012
Task: K-map Simplification
Student Name: Shaukat Mahmood (03007411855)
Registration No. 16D2-212022
Program: B-Tech Pass (Advance)
Quarter: 5th
Submitted to: Professor Assad Umer Khan
Assignment Task:
USE OF KARNAUGH MAP FOR SIMPLIFICATION OF LOGIC CIRCUIT/ EXPRESSION
Rules for Karnaugh Map Simplification:
Followings are the rules to use k-Map for logic circuit simplification 1. Enter a 1 on the Karnaugh map for each fundamental product term that corresponds to 1 output, in the truth table. Enter 0s elsewhere. 2. Encircle the octets, quads, and pairs. Remember to roll and overlap to get the largest groups possible. 3. If any isolated 1s remain, encircle them. 4. Eliminate redundant groups if any exist. 5. Indicate don’t condition, if any, with X instead of 1s or 0s. 6. Treat X as 0 or 1 to form octets, quads or pair, as per simplification requirement. 7. Write the Boolean equation by ORing the products corresponding to the encircled groups. 8. Draw the equivalent logic circuit.
Example-1: Simplify the following Boolean Equation using K-Map
Y= A’B’C’D+ A’B’CD’+ A’B’CD+ A’BC’D’+ A’BCD’+ AB’C’D’+ AB’C’D+ AB’CD’+ ABC’D’+ ABC’D+ ABCD’
Solution:
Now for
Group-I Group-II Group-IIi
ABCD ABCD ABCD
0001 1100 0010
0011 1101 0110 A’B’D 1000 1110 1001 1010 AC’ CD’
Simplified SOP is
Y=A’B’D+AC’+CD’
Example-2: Simplify the following Boolean Equation using K-Map
Y=A’BC’D’+ABC’D’+ABC’D+ABCD+ABCD’+AB’C’D’_AB’C’D+AB’CD+AB’CD’
Now for, Group-I Group-II
ABCD ABCD
0101 1100
1101 1101 BC’D 1111 1110 1000 1001 1011 1010 A
Simplified SOP equation is Y=A+BC’D
Example-3: Simplify the following Boolean Equation using K-Map