$($a$)$

FIGURE $11-24$ Sum$-$of$-$Products Example.

INTEGRATED MATH APPLICATION:

Apply the distributive law to the following Boolean expression in order to convert it into a

sum$-$of$-$products form.

$Y=\frac{A}{b}ar(B)+C(\frac{D}{b}ar(E)+\frac{F}{b}ar(G))$

Solution:

$Y=\frac{A}{b}ar(B)+C(\frac{D}{b}ar(E)+\frac{F}{b}ar(G))$ Original expression

$Y=\frac{A}{b}ar(B)+C\frac{D}{b}ar(E)+C\frac{F}{b}ar(G)$ Distributive law applied

SELF$-$TEST EVALUATION POINT FOR SECTION $11-3$

Now that you have completed this section, you should be

able to:

Objective $4.$ Describe the logic circuit design

process from truth table to gate circuit.

Objective $5.$ Explain the difference between a

sum$-$of$-$products equation and a product$-$of$-$sums

equation.

Use the following questions to test your understanding of

Section $11-3$:

A two$-$input AND gate will produce at its output the logical

of $A,$ and $B,$ while an OR gate will pro$-$

duce at its output the logical

of A and $B.$

What are the fundamental products of each of the following

input words?

a$.A,B,C,D=1011$

b$.A,B,C,D=0110$

The Boolean expression $Y=AB\frac{+}{b}ar(A)B$ is an example of a$($n$)$

$($SOP$/$POS$)$ equation.

Describe the steps involved to develop a logic circuit from a

truth table.

$11-4$ GATE CIRCUIT SIMPLIFICATION

In the last section we saw how we could convert a desired set of conditions in a truth table to

a sum$-$of$-$products equation, and then to an equivalent logic circuit. In this section we will

see how we can simplify the Boolean equation using Boolean laws and rules and therefore