Chapter 11: Problem 6
Draw a circuit using only NAND gates that computes \(x y\).
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Chapter 11: Problem 6
Draw a circuit using only NAND gates that computes \(x y\).
These are the key concepts you need to understand to accurately answer the question.
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Design a circuit with three inputs that outputs 1 precisely when two or three inputs have value \(1 .\)
Let \(*\) be a binary operator on a set \(S\) containing 0 and \(1 .\) Write a set of axioms for \(*\), modeled after rules that NAND satisfies, so that if we define $$ \begin{aligned} \bar{x} &=x * x \\ x \vee y &=(x * x) *(y * y) \\ x \wedge y &=(x * y) *(x * y) \end{aligned} $$ then \((S, \vee, \wedge,-, 0,1)\) is a Boolean algebra.
Verify the equations. $$ x_{1} \vee x_{1}=x_{1} $$
Prove or disprove the equations. $$ \left(\overline{\left(\bar{x}_{1} \wedge x_{2}\right) \vee\left(x_{1} \wedge \bar{x}_{3}\right)}\right)=\left(x_{1} \vee \bar{x}_{2}\right) \wedge\left(x_{1} \vee \bar{x}_{3}\right) $$
Tell whether the given expression is a Boolean expression. If it is a Boolean expression, use Definition 11.1 .9 to show that it is. $$ x_{1} \wedge \bar{x}_{2} \vee x_{3} $$
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