Digital Electronics and Logic Gates
6. Digital Electronics and Logic Gates
This domain tests number systems, Boolean algebra, gate truth tables, and simple combinational and sequential circuits.
Number systems and codes
- Binary weights are 8 4 2 1; convert decimal to binary by repeated division by 2, and binary to decimal by summing weights.
- BCD uses four bits per decimal digit; hexadecimal uses 0–9 and A–F.
Gates and Boolean algebra
- AND: Y = A·B (output 1 only when all inputs are 1). OR: Y = A + B. NOT: complement. NAND and NOR are universal gates.
- XOR: Y = A⊕B, 1 when the inputs differ; used in adders and parity.
- Identities: A + 0 = A, A·1 = A, A + 1 = 1, A·0 = 0, A + A = A, A·A = A, A + A' = 1, A·A' = 0.
- De Morgan: (A·B)' = A' + B' and (A + B)' = A'·B'.
- Half adder: Sum = A⊕B, Carry = A·B. A full adder also accepts a carry-in.
Sequential circuits
- Flip-flops are bistable memory elements; a clocked JK flip-flop toggles when J = K = 1.
- A counter is a chain of flip-flops; n flip-flops divide by 2ⁿ; a register stores a binary word.
Worked example
Simplify Y = A·B + A·B'. Factor out A: Y = A(B + B') = A·1 = A. The B term is redundant, so a single wire from A implements the function - two gates are saved.
Traps
- Writing OR as A·B and AND as A + B.
- Applying De Morgan without changing the operator as well as the signs.
- Confusing XOR with OR, which gives 1 for 1 + 1.
- Forgetting that NAND followed by NOT is AND, not OR.