Chapter 12: Q11E (page 818)
Prove the absorption law \({\bf{x + xy = x}}\) using the other laws in Table \(5\).
The given law \(x + xy = x\) is proved by using the other laws.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
What values of the Boolean variables \({\bf{x}}\) and \({\bf{y}}\) satisfy \({\bf{xy = x + y}}\)\(?\)
Construct a \({\bf{K}}\)-map for \({\bf{F(x,y,z) = xz + yz + xy\bar z}}{\bf{.}}\) Use this \({\bf{K - }}\)map to find the implicants, prime implicants, and essential prime implicants of \({\bf{F(x,y,z)}}\).
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.)
Which rows and which columns of a \(4{\bf{ \ast }}16\) map for Boolean functions in six variables using the Gray codes \({\bf{1111}},{\bf{1110}},{\bf{1010}},{\bf{1011}},{\bf{1001}},{\bf{1000}},{\bf{0000}},{\bf{0001}},{\bf{0011}},{\bf{0010}},{\bf{0110}},{\bf{0111}},{\bf{0101}},{\bf{0100}},{\bf{1100}},{\bf{1101}}\) to label the columns and \({\bf{11}},{\bf{10}},{\bf{00}},{\bf{01}}\) to label the rows need to be considered adjacent so that cells that represent min-terms that differ in exactly one literal are considered adjacent\(?\)
Are these sets of operators functionally complete?
a) \(\left\{ {{\bf{ + ,}} \oplus } \right\}\)
b) \(\left\{ {\,{\bf{,}} \oplus } \right\}\)
c) \({\bf{\{ \cdot,}} \oplus {\bf{\} }}\)
What do you think about this solution?
We value your feedback to improve our textbook solutions.
