5. Obtain the simplest possible logic diagram for the circuit shown below:OutputBDarDlupo ta

Answered: 5. Obtain the simplest possible logic…

Electric Motor Control

10th Edition

ISBN:9781133702818

Author:Herman

Publisher:Herman

Chapter22: Sequence Control

Section: Chapter Questions

Problem 6SQ: Draw a symbol for a solid-state logic element AND.

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Question

5. Obtain the simplest possible logic diagram for the circuit shown below:
Output
B
DarD
lupo ta

Expert Solution

Step 1

The given circuit is:

Step 2

For the given circuit the output expression can be written as,

$\begin{array}{rcl} Y \end{array} \begin{array}{rcl} = \end{array} \begin{array}{rcl} \bar{(\bar{A} + \bar{A + B}) . (\bar{B} + \bar{B + C})} \end{array}$

Now simplifying the above expression using Boolean algebra

$\begin{array}{rcl} Y & = & \bar{(\bar{A} + \bar{A + B}) . (\bar{B} + \bar{B + C})} \\ = & (\bar{\bar{A} + \bar{A + B}}) + (\bar{\bar{B} + \bar{B + C}}) [Using Demorgan' s theorem] \\ = & (\bar{\bar{A}} . \bar{\bar{A + B}}) + (\bar{\bar{B}} . \bar{\bar{B + C}}) [Using Demorgan' s theorem] \\ = & A . (A + B) + B . (B + C) \\ = & A . A + A . B + B . B + B . C \\ = & A + A B + B + B C [∵ A . A = A] \\ = & A (1 + B) + B (1 + C) \\ = & A + B [∵ 1 + B = 1 & 1 + C = 1] \end{array}$

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