Using XOR as a controlled inverter Show from the truth table how an exclusive-OR (XOR) gate can invert the data on one input when the other input acts as a control.
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AUsing A as the control, when A = 0, X is the same as B. When A = 1, X is the same as B.
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BUsing A as the control, when A = 0, X is the same as B. When A = 1, X is the inverse of B.
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CUsing A as the control, when A = 0, X is the inverse of B. When A = 1, X is the same as B.
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DUsing A as the control, when A = 0, X is the inverse of B. When A = 1, X is the inverse of B.
Answer
Correct Answer: Using A as the control, when A = 0, X is the same as B. When A = 1, X is the inverse of B.
Explanation
Introduction / Context:The XOR function is invaluable for conditional inversion. Treating one input as a control line turns XOR into a 1-bit multiplexer between “pass-through” and “invert” behaviors, used in arithmetic units and data encoding.
Given Data / Assumptions:
- XOR definition: X = A XOR B = 1 when inputs differ, 0 when equal.
- Let A be the control input; B is the data input.
- We want X to equal B when A = 0, and X to equal NOT B when A = 1.
Concept / Approach:From the XOR truth table: X = A XOR B = (NOT A AND B) OR (A AND NOT B). This directly encodes pass-through for A = 0 and inversion for A = 1.
Step-by-Step Solution:
If A = 0: X = 0 XOR B = B → pass-through.If A = 1: X = 1 XOR B = NOT B → inversion.Truth-table rows: (A,B) = (0,0)→0, (0,1)→1 (same as B); (1,0)→1, (1,1)→0 (inverted).Therefore XOR acts as a controlled inverter with A as the control.Verification / Alternative check:Algebraic rewrite: X = B XOR A = B when A = 0; X = NOT B when A = 1. Hardware implementations of adders use this to conditionally complement operands.
Why Other Options Are Wrong:
- Same as B for both A values: Ignores XOR behavior; that would be a buffer.
- Inverse when A = 0 and same when A = 1: Reversed from XOR’s property.
- Inverse for both A values: That would be a pure inverter, not controlled.
Common Pitfalls:Swapping the role of control and data, or confusing XOR with XNOR (which is equality, not inversion control).
Final Answer:Using A as the control, when A = 0, X is the same as B. When A = 1, X is the inverse of B.