Which of the following set of components is sufficient to implement any…
2017
Which of the following set of components is sufficient to implement any arbitrary Boolean function?
a) XOR gates, NOT gates
b) 2 to 1 multiplexers
c) AND gates, XOR gates, 1
d) Three-input gates that output (A.B)+C for the inputs A, B and C.
- A.
a and d
- B.
b and c
- C.
c
- D.
All a, b, c and d
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Correct answer: B
A set of logic gates is functionally complete if it can implement any Boolean function. Option 'a' (XOR and NOT) cannot generate AND or OR operations, as XOR is linear and lacks the ability to create non-linear functions like AND without constants. Option 'b' (2-to-1 multiplexers) is functionally complete because any Boolean function can be implemented using a MUX by selecting appropriate inputs. Option 'c' (AND, XOR, and constant 1) is also complete since AND with a constant allows generating NOT (via A·1 = A, and using XOR to invert), enabling full logic synthesis. Option 'd' (three-input gates) is not inherently complete without additional context. Therefore, only sets b and c are sufficient.
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