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

For these two truth tables

Truth Table 1: Truth Table 2:

A B C --> Output A B C D --> Output

0 0 0 --> 1    0 0 0 0 --> 1

0 0 1 --> 1    0 0 0 1 --> 0

0 1 0 --> 0    0 0 1 0 --> 1

0 1 1 --> 0    0 0 1 1 --> 0

1 0 0 --> 0    0 1 0 0 --> 0

1 0 1 --> 0    0 1 0 1 --> 1

1 1 0 --> 1      0 1 1 0 --> 0

1 1 1 --> 1      0 1 1 1 --> 1

   1 0 0 0 --> 1

     1 0 0 1 --> 0

       1 0 1 0 --> 1

       1 0 1 1 --> 0

       1 1 0 0 --> 0

       1 1 0 1 --> 1

       1 1 1 0 --> 0

       1 1 1 1 --> 1

Part a) Give the sum of products of Truth Table 1

Part b) Reduce the equation in Part a) using the rules of Boolean Algebra to find the most simplified version of the sum of products.

Part c) Give the sum of products of Truth Table 2

Part d) Reduce the equation in Part c) using the rules of Boolean Algebra to find the most simplified version of the sum of products.

For Part b) and Part d) make sure you show every step you performed in the reduction to the simplified sum of product equations.

Answer 1