Chapter 12: Q2E (page 827)
In Exercises 1–5 find the output of the given circuit.
Short Answer
The output of the circuit is (x +y).
Chapter 12: Q2E (page 827)
In Exercises 1–5 find the output of the given circuit.
The output of the circuit is (x +y).
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Get started for free\(a)\) Draw a \(K{\bf{ - }}\)map for a function in two variables and put a \(1\) in the cell representing \(\bar xy\).
\(b)\)What are the minterms represented by cells adjacent to this cell\(?\)
Let \({\bf{x}}\) and \({\bf{y}}\) belong to \(\left\{ {{\bf{0,1}}} \right\}\). Does it necessarily follow that \({\bf{x = y}}\) if there exists a value \({\bf{z}}\) in \(\left\{ {{\bf{0,1}}} \right\}\) such that,
\(\begin{array}{l}{\bf{a) xz = yz?}}\\{\bf{b) x + z = y + z?}}\\{\bf{c) x}} \oplus {\bf{z = y}} \oplus {\bf{z?}}\\{\bf{d) x}} \downarrow {\bf{z = y}} \downarrow {\bf{z?}}\\{\bf{e) x}}|{\bf{z = y}}|z{\bf{?}}\end{array}\)
A Boolean function \({\bf{F}}\) is called self-dual if and only if \({\bf{F}}\left( {{{\bf{x}}_{\bf{1}}}{\bf{, \ldots ,}}{{\bf{x}}_{\bf{n}}}} \right){\bf{ = }}\overline {{\bf{F}}\left( {{{{\bf{\bar x}}}_{\bf{1}}}{\bf{, \ldots ,}}{{{\bf{\bar x}}}_{\bf{n}}}} \right)} \).
Show that if \(F\) and \(G\) are Boolean functions of degree \(n\), then
\(\begin{array}{l}a)F \le F{\bf{ + }}G\\b)FG \le F\end{array}\)
Construct a \({\bf{K}}\)-map for \({\bf{F(x,y,z) = xz + yz + xy\bar z}}\). Use this \({\bf{K}}\)-map to find the implicants, prime implicants, and essential prime implicants of \({\bf{F(x,y,z)}}\).
Is it always true that \((x \odot y) \odot z{\bf{ = }}x \odot (y \odot z)\)\(?\)
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