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Chapter 12: Q1E (page 827)

In Exercises 1–5 find the output of the given circuit.

Short Answer

Expert verified

The output of the circuit is\({\bf{(x + y)}}\overline {\bf{y}} \).

Step by step solution

01

Defining of gates

There are three types of gates.

It is also called NOT gate.

02

Find the output.

The first gate is OR gate (x +y) and gate below is not. Therefore, the output is the AND combination of (x +y) and\(\overline {\bf{y}} \).

Therefore, the output of the circuit is\({\bf{(x + y)}}\overline {\bf{y}} \).

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Most popular questions from this chapter

Draw the \({\bf{K}}\)-maps of these sum-of-products expansions in three variables.

\(\begin{array}{l}{\bf{a) x\bar y\bar z}}\\{\bf{b) \bar xyz + \bar x\bar y\bar z}}\\{\bf{c) xyz + xy\bar z + \bar xy\bar z + \bar x\bar yz}}\end{array}\)

Show how the sum of two five-bit integers can be found using full and half adders.

Find the duals of these Boolean expressions.

\(\begin{array}{l}{\bf{a) x + y}}\\{\bf{b) \bar x\bar y}}\\{\bf{c) xyz + \bar x\bar y\bar z}}\\{\bf{d) x\bar z + x \times 0 + \bar x \times 1}}\end{array}\)

Find the sum-of-products expansion of the Boolean function F (\({{\bf{x}}_{\bf{1}}}{\bf{,}}{{\bf{x}}_{\bf{2}}}{\bf{,}}{{\bf{x}}_{\bf{3}}}{\bf{,}}{{\bf{x}}_{\bf{4}}}{\bf{,}}{{\bf{x}}_{\bf{5}}}\)) that has the value 1 if and only if three or more of the variables \({{\bf{x}}_{\bf{1}}}{\bf{,}}{{\bf{x}}_{\bf{2}}}{\bf{,}}{{\bf{x}}_{\bf{3}}}{\bf{,}}{{\bf{x}}_{\bf{4}}}{\bf{,}}{{\bf{x}}_{\bf{5}}}\) have the value 1.

Find a Boolean product of Boolean sums of literals that has the value 0 if and only if \({\bf{x = y = 1}}\) and \({\bf{z = 0,x = z = 0}}\) and \({\bf{y = 1}}\), or \({\bf{x = y = z = 0}}\). (Hint: Take the

Boolean product of the Boolean sums found in parts (a), (b), and (c) in Exercise 7.)
See all solutions

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