The K-map below for y = f(a,b,c) defines each cell of the K-map by letters S-Z. Which of the 3-input minterms below is correctly associated with the correct K-map cell S-Z? Select all that apply; scored equally weighted.

Question

BlackTom AI · Accepted Answer

We start by restating the problem in our own words to ensure clarity: we have a 3-variable K-map for y = f(a,b,c) with cells labeled S through Z, and we are to identify which of the given minterms correspond to the labeled cells. The provided available answer indicates that Z = abc'. We must evaluate each option against the assumed K-map labeling.

Option 1: T = a'bc'
- This minterm corresponds to a = 0, b = 1, c = 0. In decimal terms, that’s m2 (since m = 4a + 2b + c, here 0*4 + 1*2 + 0 = 2).
- Without the explicit mapping of S–Z to minterms shown in the K-map, we rely on the standard idea that each cell S–Z is supposed to represent a unique minterm. Since the claimed correct association in the problem statement is Z = abc', T would have to correspond to a different minterm (m2) and thus would occupy a different cell, not Z. Therefore, T = a'bc' is unlikely to be correct for cell Z, and this option is incorrect with respect to the Z labeling.

Option 2: X = ab'c'
- This minterm corresponds to a = 1, b = 0, c = 0, i.e., m4 (since 1*4 + 0*2 + 0 = 4).
- Similar to the previous reasoning, if Z is specifically labeled abc', then X would map to the minterm m4 and a different cell. Unless the K-map labeling placed m4 at cell X and Z at m6, this option would be inconsistent with Z = abc'. Hence this option is incorrect with respect to the Z cell labeling.

Option 3: Z = abc'
- This directly states that cell Z corresponds to the minterm with a = 1, b = 1, c' = 1, i.e., c = 0, which is the minterm m6 (since 1*4 + 1*2 + 0 = 6).
- If the problem’s given answer asserts Z = abc', then this option aligns exactly with that specified labeling. Therefore, this option is correct for the Z cell.

Option 4: V = a'b'c'
- This minterm corresponds to a = 0, b = 0, c = 0, i.e., m0.
- As with the other non-Z options, unless the K-map’s S–Z labeling places m0 specifically at V, this would not be the same as Z’s assignment. Given the instruction that Z corresponds to abc' (m6), V = a'b'c' (m0) would be a different cell, making this option incorrect with respect to the Z labeling.

In summary, when identifying which minterms correspond to the labeled cells, only the statement Z = abc' correctly matches the cell Z to its minterm according to the provided (or implied) labeling. The other options assign different minterms to different cells (T to m2, X to m4, V to m0), which would not be consistent with Z being abc'.

The K-map below for y = f(a,b,c) defines each cell of the K-map by letters S-Z. Which of the 3-input minterms below is correctly associated with the correct K-map cell S-Z? Select all that apply; scored equally weighted.

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