Name:Boolean Worksheet 3 Karnaugh Maps

Computer Science IF862Boolean Algebra and Propositional Logic

Name:Boolean Worksheet 3 – Karnaugh Maps

Criterion 4 – Demonstrate knowledge and understanding of computer architecture.

1. Determine the Boolean expression for each of the following Karnaugh Maps.

B
0 / 1
A / 0
1 / 1

Computer Science IF862Boolean Algebra and Propositional Logic

B
0 / 1
A / 0
1 / 1

Computer Science IF862 Boolean Algebra and Propositional Logic

Computer Science IF862 Boolean Algebra and Propositional Logic

B
0 / 1
A / 0
1 / 1 / 1
B
0 / 1
A / 0 / 1
1 / 1
C
0 / 1
0 / 0
A / 0 / 1 / B
1 / 1 / 1
1 / 1 / 0
C
0 / 1
0 / 1 / 1 / 0
A / 0 / 1 / B
1 / 1
1 / 0

1. Fill in the Karnaugh maps for the following expressions

a ᴠ b

B
0 / 1
A / 0
1

(aᴧb)ᴠ(aᴧc)

C
0 / 1
0 / 0
A / 0 / 1 / B
1 / 1
1 / 0

(aᴧb) ᴠ (aᴧ~b)

B
0 / 1
A / 0
1

(aᴠb)ᴠ(bᴧ~c)

C
0 / 1
0 / 0
A / 0 / 1 / B
1 / 1
1 / 0

1. Convert the truth table to a Karnaugh map and then to the relevant expression

A / B / C / D / F
0 / 0 / 0 / 0 / 0
0 / 0 / 0 / 1 / 0
0 / 0 / 1 / 0 / 0
0 / 0 / 1 / 1 / 0
0 / 1 / 0 / 0 / 0
0 / 1 / 0 / 1 / 0
0 / 1 / 1 / 0 / 1
0 / 1 / 1 / 1 / 0
1 / 0 / 0 / 0 / 0
1 / 0 / 0 / 1 / 0
1 / 0 / 1 / 0 / 0
1 / 0 / 1 / 1 / 1
1 / 1 / 0 / 0 / 0
1 / 1 / 0 / 1 / 0
1 / 1 / 1 / 0 / 1
1 / 1 / 1 / 1 / 1
C
0 / 0 / 1 / 1
0 / 0
A / 0 / 1 / B
1 / 1
1 / 0
0 / 1 / 1 / 0
D

1. Write the Boolean expressions for the following K-maps:

C
0 / 0 / 1 / 1
0 / 1 / 0
A / 0 / 1 / B
1 / 1
1 / 0
0 / 1 / 1 / 0
D
C
0 / 0 / 1 / 1
0 / 0
A / 0 / 1 / B
1 / 1 / 1 / 1
1 / 1 / 1 / 0
0 / 1 / 1 / 0
D
C
0 / 0 / 1 / 1
0 / 1 / 0
A / 0 / 1 / 1 / 1 / B
1 / 1 / 1
1 / 0
0 / 1 / 1 / 0
D
C
0 / 0 / 1 / 1
0 / 1 / 0
A / 0 / 1 / 1 / B
1 / 1
1 / 0
0 / 1 / 1 / 0
D

1. Fill in the Karnaugh maps for the expressions.

C
0 / 0 / 1 / 1
0 / 0
A / 0 / 1 / B
1 / 1
1 / 0
0 / 1 / 1 / 0
D

~a ᴧ ~b

C
0 / 0 / 1 / 1
0 / 0
A / 0 / 1 / B
1 / 1
1 / 0
0 / 1 / 1 / 0
D

(~aᴧ~cᴧ~d) ᴠ (aᴧbᴧ~d)

1. Draw alogiccircuit to implement the following truth table:

A / B / C / Output
0 / 0 / 0 / 0
0 / 0 / 1 / 0
0 / 1 / 0 / 0
0 / 1 / 1 / 1
1 / 0 / 0 / 0
1 / 0 / 1 / 1
1 / 1 / 0 / 1
1 / 1 / 1 / 0
A / B / X
0 / 0 / 0
0 / 1 / 0
1 / 0 / 1
1 / 1 / 1

1. A function X has thistruth table. Draw a K-map for the function and use the K-map to simplify the function.

A / B / C / X
0 / 0 / 0 / 0
0 / 0 / 1 / 0
0 / 1 / 0 / 1
0 / 1 / 1 / 1
1 / 0 / 0 / 1
1 / 0 / 1 / 1
1 / 1 / 0 / 0
1 / 1 / 1 / 0

1. A function X in three variables has this truth table.
   a) Simplify the function using a K-map.
   b) Show how this function can be implemented as a circuit containing and,or, and notgates.