Chapter 12: Q16E (page 828)
Use NOR gates to construct circuits for the outputs given
in Exercise 15.
Short Answer
The results are
(a)
(b)
(c)
(d)
Chapter 12: Q16E (page 828)
Use NOR gates to construct circuits for the outputs given
in Exercise 15.
The results are
(a)
(b)
(c)
(d)
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Get started for freeIs there a single type of logic gate that can be used to build all circuits that can be built using \({\bf{OR}}\)gates, \({\bf{AND}}\) gates, and inverters?
Prove the absorption law \({\bf{x + xy = x}}\) using the other laws in Table \(5\).
Use a \(K{\bf{ - }}\)map to find a minimal expansion as a Boolean sum of Boolean products of each of these functions of the Boolean variables \({\bf{x}}\) and \({\bf{y}}\).
\(\begin{array}{l}{\bf{a)\bar xy + \bar x\bar y}}\\{\bf{b)xy + x\bar y}}\\{\bf{c)xy + x\bar y + \bar xy + \bar x\bar y}}\end{array}\)
use the laws in Definition \(1\) to show that the stated properties hold in every Boolean algebra.
Show that in a Boolean algebra, the modular properties hold. That is, show that \({\bf{x}} \wedge {\bf{(y}} \vee {\bf{(x}} \wedge {\bf{z)) = (x}} \wedge {\bf{y)}} \vee {\bf{(x}} \wedge {\bf{z)}}\) and \({\bf{x}} \vee {\bf{(y}} \wedge {\bf{(x}} \vee {\bf{z)) = (x}} \vee {\bf{y)}} \wedge {\bf{(x}} \vee {\bf{z)}}\).
Show that cells in a \({\bf{K}}\)-map for Boolean functions in five variables represent minterms that differ in exactly one literal if and only if they are adjacent or are in cells that become adjacent when the top and bottom rows and cells in the first and eighth columns, the first and fourth columns, the second and seventh columns, the third and sixth columns, and the fifth and eighth columns are considered adjacent.
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