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Solutions to Digital Logic Exercises

These are the solutions to the digital logic exercises. You are strongly advised to work out your own solutions before you look at these.

1. Given the function defined by the truth table below, derive the sum of products expression and draw the corresponding circuit diagram.

A B Output
0 0 1
0 1 0
1 0 0
1 1 0

Output = (~A)(~B) 

2. Given the function defined by the truth table below, derive the sum of products expression and draw the corresponding circuit diagram.

A B Output
0 0 1
0 1 1
1 0 1
1 1 0

Output = (~A)(~B) + (~A)B + A(~B)

3. Given the function defined by the truth table below, derive the sum of products expression and draw the corresponding circuit diagram.

A B C Output
0 0 0 1
0 0 1 1
0 1 0 0
0 1 1 0
1 0 0 1
1 0 1 0
1 1 0 0
1 1 1 0

Output = (~A)(~B)(~C) + (~A)(~B)C + A(~B)(~C) 

Circuit Diagram 

4. Given the function defined by the truth table below, derive the sum of products expression and draw the corresponding circuit diagram.

A B C Output
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0

~A~BC + ~ABC + A~B~C + AB~C

Circuit Diagram