Chapter 12: Q4E (page 827)
In Exercises 1–5 find the output of the given circuit.
Short Answer
The output of the circuit is\(\overline {{\bf{xyz}}} {\bf{(x + y + z)}}\).
Chapter 12: Q4E (page 827)
In Exercises 1–5 find the output of the given circuit.
The output of the circuit is\(\overline {{\bf{xyz}}} {\bf{(x + y + z)}}\).
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Get started for freeShow that you obtain De Morgan's laws for propositions (in Table \(6\) in Section \(1.3\)) when you transform De Morgan's laws for Boolean algebra in Table \(6\) into logical equivalences.
Use a \({\bf{K}}\)-map to find a minimal expansion as a Boolean sum of Boolean products of each of these functions in the variables \({\bf{w, x, y}}\) and \({\bf{z}}\).
\(\begin{array}{l}{\bf{a) wxyz + wx\bar yz + wx\bar y\bar z + w\bar xy\bar z + w\bar x\bar yz}}\\{\bf{b) wxy\bar z + wx\bar yz + w\bar xyz + \bar wx\bar yz + \bar w\bar xy\bar z + \bar w\bar x\bar yz}}\\{\bf{c) wxyz + wxy\bar z + wx\bar yz + w\bar x\bar yz + w\bar x\bar y\bar z + \bar wx\bar yz + \bar w\bar xy\bar z + \bar w\bar x\bar yz}}\\{\bf{d) wxyz + wxy\bar z + wx\bar yz + w\bar xyz + w\bar xy\bar z + \bar wxyz + \bar w\bar xyz + \bar w\bar xy\bar z + \bar w\bar x\bar yz}}\end{array}\)
Is it always true that \((x \odot y) \odot z{\bf{ = }}x \odot (y \odot z)\)\(?\)
Show that \({\bf{x}} \odot {\bf{y = xy + \bar x\bar y}}\).
Find a Boolean product of the Boolean variables x, y,and z, or their complements, that has the value 1 if and only if
a)x=y=0, z=1
b)x=0, y=1, z=0
c)x=0, y=z=1
d)x=y=z=0
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