Consider the 4-variable Boolean function
$F (w, x, y, z) = Σ m (0, 2, 5, 7, 8, 10, 13, 15)$
where $w$ is the most significant bit and $z$ the least significant bit, and there are no don't-care terms. Which one of the following is the minimal sum-of-products form of $F$ ?

(Here $^{'}$ denotes complement.)

Question

Consider the 4-variable Boolean function

F (w, x, y, z) = Σ m (0, 2, 5, 7, 8, 10, 13, 15)

where $w$ is the most significant bit and $z$ the least significant bit, and there are no don't-care terms. Which one of the following is the minimal sum-of-products form of $F$ ?

(Here $^{'}$ denotes complement.)

Accepted Answer

(A) x'z' + xz. Method: place the minterms on the K-map and take the largest groups. With rows wx and columns yz in Gray order (00, 01, 11, 10): wx yz 00 01 11 10 00 1 (m0) 1 (m2) 01 1 (m5) 1 (m7) 11 1 (m13) 1 (m15) 10 1 (m8) 1 (m10) - m0, m2, m8, m10 are the four corners. The map wraps left-right and top-bottom, so they form one group of four where x = 0 and z = 0: the term x'z'. - m5, m7, m13, m15 form the…

Answer

x'z + xz'

Answer

w'x'z' + wx'z' + xz

Answer

x'z' + xyz

Minimization and K-maps: GATE CS question with solution

Solution MCQ · 2 marks · −⅔ if wrong