Which one of the following circuits implements the Boolean function given…
2021
Which one of the following circuits implements the Boolean function given below?
\(f(x,y,z) = m_0+m_1+m_3+m_4+m_5+m_6\) where \(m_i \) is the \(i^{th}\) minterm.
Attempted by 98 students.
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Key idea: implement the function with a 4-to-1 MUX using s1 = y and s0 = z.
yz = 00 (D0): minterms m0 and m4 → f = 1, so D0 = 1.
yz = 01 (D1): minterms m1 and m5 → f = 1, so D1 = 1.
yz = 10 (D2): minterms m2 (x=0) and m6 (x=1) → f = x, so D2 = x.
yz = 11 (D3): minterms m3 (x=0) and m7 (x=1) → f = x', so D3 = x'.
Therefore the MUX data inputs should be D0..D3 = 1, 1, x, x' (respectively) with s1 = y and s0 = z. This matches the given function. A compact Boolean form is f = y' + (x XOR z).
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