What two numbers have the sum of 12 and the difference of 4
2 answers:
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Answer:
a) the K-map is in the attachment
<em>f = Σ</em>m(0,1,2,3,6,10,14,15)
b) from the k-map, the minimum sum of products is
F = A'B' + CD' + ABC
c) the minimum product of sums is
F = (B' + C)(A' + C)(A+ B' +D')(A' + B + D')
Step-by-step explanation:
A Karnaugh map (K-map) is a pictorial framework used to limit the Boolean expressions without utilizing Boolean algebra theorems and equation controls.
a) the given function is <em>f</em>(A,B,C,D)=A‘B’+CD’+ABC +A’B’CD’+ABCD’
expanding the function as four variable terms
<em>f</em>(A,B,C,D)=A‘B’+CD’+ABC +A’B’CD’+ABCD’
= A'B'(C + C')(D + D')+(A + A')(B + B")CD' + ABC(D + D') + A'B'CD' + ABCD'
= A'B'CD + A'B'CD' + A'B'C'D' + ABCD' +AB'CD' + A'BCD' + A'B'CD' + ABCD +ABCD' + A'B'CD' + ABCD'
=A'B'CD + A'B'CD' + A'B'C'D + A'B'C'D' + ABCD' + AB'CD' + A'BCD' +ABCD
<em>f = Σ</em>m(0,1,2,3,6,10,14,15)
note: diagram is in the attachment
b) the minterms for the minimum sum of product are
<em>f = Σ</em>m(0,1,2,3,6,10,14,15)
simplifying the K-map(done in the attachment)
from the k-map, the minimum sum of products is
F = A'B' + CD' + ABC
c) the maxterms for the minimum product of sums are
<em>f </em>= ПM(4,5,7,8,9,11,12,13)
plot the K-map to find minimum product of sums(done in the attachment)
the minimum product of sums is
F = (B' + C)(A' + C)(A+ B' +D')(A' + B + D')
