Boolean Algebra and Universal Gates
NAND and NOR are universal gates because each can realize NOT, AND, and OR. De Morgan's laws relate complemented products and sums and support systematic circuit simplification.
Why this shows up in the exam
Simplifying gate networks · Implementing functions with only NAND gates · Implementing functions with only NOR gates
Learn the idea
Boolean identities and De Morgan's laws reduce circuits and show that NAND or NOR alone can build any logic function. Moving a NOT operation through an AND or OR changes the operation and complements the inputs. This bubble-pushing view makes many complicated gate networks simpler.
🧠 Memory hook: Push a bar through: swap AND and OR, and bar each input.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- overline(A B) = overline(A) + overline(B) — De Morgan's law for a complemented product
- overline(A + B) = overline(A) overline(B) — De Morgan's law for a complemented sum
- A NAND A = overline(A); A NOR A = overline(A) — creating NOT with a universal gate
How to approach it
- 1Write the expression at each gate output
- 2Apply De Morgan's law to complete grouped terms
- 3Verify the final expression with a short truth table
Common slip-ups that cost marks
- •Changing AND to OR without complementing every input
- •Treating a double complement as a remaining NOT
- •Simplifying a diagram without preserving fan-out paths
🌟 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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