Digital Electronics and Logic
Digital electronics tests number systems, Boolean algebra, logic gates, and simple combinational and sequential circuits. The emphasis is on correct conversion and simplification, not memorising long tables.
Core facts
- Binary place values are powers of 2: 8, 4, 2, 1 for four bits. Hexadecimal uses 0–9 and A–F.
- Basic gates: AND, OR, NOT. Derived gates: NAND, NOR, XOR. NAND and NOR are universal gates.
- Boolean identities include A + 0 = A, A · 1 = A, A + A = A, A · A = A, A + A·B = A, and A + A′ = 1.
- De Morgan: (A·B)′ = A′ + B′ and (A + B)′ = A′·B′.
- Combinational circuits include adders and multiplexers; sequential circuits include flip-flops and counters and use memory/clock.
Worked example
Simplify Y = A + A·B. Factor A: Y = A(1 + B). Since 1 + B = 1, Y = A. This is the absorption law. A truth-table check confirms it: when A = 1, Y = 1 regardless of B; when A = 0, both terms are 0. For a conversion example, binary 1101 = 1×8 + 1×4 + 0×2 + 1×1 = 13 in decimal, which is D in hexadecimal.
Traps
- Reading binary digits in the wrong order; the leftmost is the highest place value.
- Applying De Morgan without changing the operation sign.
- Treating XOR as the same as OR; XOR is 1 only when inputs differ.
- Calling a flip-flop combinational; it is sequential and clock-dependent.