Computer Science

Convert (X' + Y + Z').(X + Y' + Z).(X + Y + Z').(X + Y + Z) into SOP form.

Boolean Algebra

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Answer

Converting to max term designation:

Binary Pattern of max term (X' + Y + Z') = 101
Decimal Equivalent of 101 = 5
Max term designation of (X' + Y + Z') = M5

Binary Pattern of max term (X + Y' + Z) = 010
Decimal Equivalent of 010 = 2
Max term designation of (X + Y' + Z) = M2

Binary Pattern of max term (X + Y + Z') = 001
Decimal Equivalent of 001 = 1
Max term designation of (X + Y + Z') = M1

Binary Pattern of max term (X + Y + Z) = 000
Decimal Equivalent of 000 = 0
Max term designation of (X + Y + Z) = M0

Max term designation = M0, M1, M2, M5
Min term designation = m3, m4, m6, m7

m3 = 011 = X'YZ
m4 = 100 = XY'Z'
m6 = 110 = XYZ'
m7 = 111 = XYZ

SOP Expression = X'YZ + XY'Z' + XYZ' + XYZ

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