XOR, XNOR, and Combinational Logic
For two inputs, XOR is the sum of the mutually exclusive products A bar B and A B bar. XNOR is its complement and represents binary equality.
Why this shows up in the exam
Binary comparison · Half-adder sum output · Recognizing crossed inverter-and-AND networks
Learn the idea
XOR detects unequal inputs, XNOR detects equal inputs, and larger combinational circuits are solved through intermediate expressions. XOR is high when exactly one of two inputs is high; XNOR is high when both match. These patterns appear in comparators, reversible operations, and crossed AND-OR networks.
🧠 Memory hook: XOR means different; XNOR means same.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- A XOR B = overline(A) B + A overline(B) — two-input exclusive-OR expression
- A XNOR B = A B + overline(A) overline(B) — two-input equality expression
How to approach it
- 1Test inputs 00 and 11 first to distinguish equality behavior
- 2Write complementary product terms
- 3Evaluate every intermediate signal for multi-stage circuits
Common slip-ups that cost marks
- •Treating XOR as ordinary OR when both inputs are 1
- •Calling XNOR reversible without checking the full operation
- •Guessing a diagram from OCR fragments instead of preserving review status
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A transistor has common-emitter current gain beta = 50. If base current is 20 microA, find collector current.
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