Boolean Algebra and Logic Gates
Boolean Algebra and Logic Gates tests the algebra of 0 and 1: the basic laws, De Morgan's theorems, truth tables, gate behaviour, universal gates, and canonical SOP/POS forms.
Core rules
- The three basic operations are OR (+), AND (·) and NOT (′). Precedence is NOT, then AND, then OR, unless brackets say otherwise.
- Identity: A + 0 = A, A · 1 = A. Domination: A + 1 = 1, A · 0 = 0. Idempotent: A + A = A, A · A = A.
- Complement: A + A′ = 1, A · A′ = 0. Involution: (A′)′ = A. Absorption: A + AB = A.
- De Morgan: (A + B)′ = A′ · B′ and (A · B)′ = A′ + B′.
- NAND and NOR are universal gates because either one alone can build AND, OR and NOT.
- XOR gives 1 when the number of 1 inputs is odd; XNOR gives 1 when inputs are equal.
- A minterm contains every variable exactly once; canonical SOP is the sum of the 1-minterms, and POS is the product of the 0-maxterms.
Worked example
Simplify F = A′B + AB + AB′. First, A′B + AB = B(A′ + A) = B. Then F = B + AB′ = (B + A)(B + B′) = (A + B)(1) = A + B. A quick truth-table check confirms F is 0 only when A = 0 and B = 0, which is exactly the OR function.
Traps that cost marks
- Applying De Morgan and changing only one side: both the operator and each term must change.
- Treating A + A′B as A only; the correct simplification is A + B.
- Confusing XOR with OR: 1 XOR 1 = 0, but 1 OR 1 = 1.
- Writing a canonical SOP term that omits a variable.
- Forgetting that NAND is AND followed by NOT, not the same as AND.