Digital Electronics and Logic Fundamentals
Digital Electronics and Logic Fundamentals tests number systems, logic gates, Boolean reduction and the difference between combinational and sequential circuits. Questions usually combine a conversion with a truth table or a simplification.
Rules to know cold
- Binary place values 8 4 2 1; hex digits 0–9 then A–F. Group four bits to convert binary to hex.
- BCD encodes each decimal digit in four bits; it is not the same as binary (e.g. 25 decimal = 0010 0101 in BCD, 11001 in binary).
- Gates: AND (product), OR (sum), NOT, NAND, NOR, XOR (output 1 when inputs differ), XNOR.
- NAND and NOR are universal gates - any circuit can be built from either alone.
- De Morgan: (A·B)′ = A′ + B′ and (A + B)′ = A′·B′.
- Combinational circuits (adders, multiplexers, decoders) have no memory; sequential circuits (flip-flops, counters, registers) do, and are clocked.
Worked example
Simplify Y = Σ(1, 3, 5, 7) for inputs A, B, C (A most significant).
Reasoning: minterm 1 = A′B′C, 3 = A′BC, 5 = AB′C, 7 = ABC. Factor C: Y = C(A′B′ + A′B + AB′ + AB) = C·1 = C. The same result appears on a Karnaugh map as one group of four adjacent cells, which is why the answer is a single variable. Showing the grouping or the factoring is what earns full credit.
Traps that cost marks
- Converting BCD as if it were pure binary.
- Applying De Morgan without changing the operator as well as the signs.
- Treating a flip-flop as combinational - its output depends on the previous state.