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.
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
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