Question

1. write a truth table using this symbol: -->

2. write the inputs for the truth table to the left of the --> and write the outputs for the truth table to the right of the -->

3. write the compliment, or NOT using '

As an example:

The truth table for AND is written this way:

A B --> A AND B

0 0 --> 0

0 1 --> 0

1 0 --> 0

1 1 --> 1

or this way:

A B --> A AND B

a' b' --> 0

a' b --> 0

a b' --> 0

a b --> 1

As another example:

For a 3 input, 2 output truth table, the truth table is written this way:

A B C --> X Y

0 0 0 --> 0 0

0 0 1 --> 1 0

0 1 0 --> 1 0

0 1 1 --> 0 1

1 0 0 --> 1 0

1 0 1 --> 0 1

1 1 0 --> 0 1

1 1 1 --> 1 1

Part a) Write the truth table for A NAND B

Part b) Write the truth table for A NOR B

Part c) Write the truth table for NOT A OR NOT B

Part d) Write the truth table for NOT A AND NOT B

Part e) Explain in English how DeMorgan's Theorem can be explained by the truth tables made for parts a, b, c, and d. Write your explanation in 8 sentences or less.

Answer 1

a)

A B --> A NAND B

0 0 --> 1

0 1 --> 1

1 0 --> 1

1 1 --> 0

b)

A B --> A NOR B

0 0 --> 1

0 1 --> 0

1 0 --> 0

1 1 --> 0

c)

A B --> NOT A OR NOT B

0 0 --> 1

0 1 --> 1

1 0 --> 1

1 1 --> 0

d)A B --> NOT A AND NOT B

0 0 --> 1

0 1 --> 0

1 0 --> 0

1 1 --> 0

e)

A NAND D = (A.B)'

APPLYING DEMORGAN THEROM

(A.B)'=A' + B' = NOT A OR NOT B

SO a and c are equal

A NOR B= (A + B)'

APPLYING DEMOORGAN THEOREM

(A+B)'= A'.B' = NOT A AND NOT B

SO b and d are equal