k-map
DESCRIPTION
sevral problems in k-mapsTRANSCRIPT
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King Saud University College of Engineering
EE 208 Logic Design
Homework 3 Solution 1- Use a K-Map to find the minimum SOP of the following Boolean functions. For
each function, find all PIs and EPIs.
a. F(a,b,c) = (a + b)c + abc F = ac + bc + abc K-Map: (Distinguished 1-cells are shaded)
PIs: ac, bc EPIs: ac, bc
F = ac + bc
b. F(a,b,c,d) = a(b + bd) + (ad + bcd)
F = ab + abd + (a + d)(b + c + d) = ab + abd + ab + ac + ad + bd + cd + d
PIs: a, b, c, d EPIs: a, b, c, d
F = a + b + c + d
c. F = a,b,c,d (0,2,4,6,7,8,11,12,15)
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PIs: cd, ad, abc, bcd, acd EPIs: cd, ad, acd
F = ad + cd + acd + bcd or F = ad + cd + acd + abc
d. F = a,b,c,d (1,3,4,5,10,11,12,13,14,15)
PIs: bc, ab, ac, acd, abd, bcd EPIs: bc, ac
F = ac + bc + abd
e. F = a,b,c,d (5,7,13,14,15)
PIs: bd, abc EPIs: bd, abc
F = bd + abc f. F = a,b,c,d (0,7,8,9,12,13,15)
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PIs: cdb, ac, abd, bcd EPIs: cdb, ac, bcd
F = cdb+ ac+ bcd
g. F = a,b,c,d (0,1,3,4,12,13,14,15)
PIs: ab, abd, abc, acd, bcd EPIs: ab, abd
F = ab + abd+acd
h. F = a,b,c,d (1,3,5,7,14,15)
PIs: ad, abc, bcd EPIs: ad, abc,
F = ad + abc
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i. F = w,x,y (1,4,5,6,7)
PIs: wy, wx EPIs: wy, wx
F = wy+ wx 2- Find two minimum SOPs for each of the following functions
a. F = a,b,c (0,2,3,4,5,7)
Red PIs: F = ac + bc + ab Green PIs: F = bc + ab + ac Notice that, there are no EPIs.
b. F = a,b,c,d (0,1,2,4,5,7,11,15)
F = ac + abd + acd + abd Or F = ac + abd + acd + bcd
3- Using a K-Map, prove that:
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ac + abc + abcd + abd = a
4- Use a K-Map to find the minimum SOP of the following Boolean functions.
a. F = a,b,c,d (0,2,4,6,7,8,11,12,15)+d(1,3,5,9)
PIs: cd, a, cd EPIs: cd, a, cd
F = cd+ a+ cd
b. F = a,b,c,d (1,3,4,5,10,11,12,13,14,15)+d(7)
PIs: bc, ad, bd, ac, ab, cd EPIs: bc, ad, ac
F = bc+ ad+ ac
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c. F = a,b,c,d (5,7,13,14,15)+d(6)
PIs: bd, bc EPIs: bd, bc
F = bd+ bc
d. F = a,b,c,d (0,7,8,9,12,13,15)+d(1,2,3)
PIs: ab, bc,ac, abd, acd, bcd, EPIs: ac
F = ac+ab+bcd or F = ac+bc+bcd