Digital Electronics and Logic Gates
What this domain covers
Digital Electronics and Logic Gates covers number systems, Boolean algebra, gate truth tables, combinational blocks and simple sequential circuits. Questions test conversion, simplification and gate-equivalent reasoning.
Core rules
- Binary place values are 1, 2, 4, 8, 16 …; BCD encodes each decimal digit in four bits; hexadecimal uses 0–9 and A–F.
- Basic gates: AND (output 1 only when all inputs are 1), OR (output 1 when any input is 1), NOT, NAND, NOR, XOR (output 1 when inputs differ) and XNOR.
- NAND and NOR are universal gates: either alone can build every other gate.
- De Morgan: (A·B)′ = A′ + B′ and (A + B)′ = A′·B′.
- A half adder has sum = A ⊕ B and carry = A·B; a full adder also adds a carry-in. Flip-flops store one bit; counters and shift registers are built from them.
Worked example
Convert 1101₂ to decimal: 1×8 + 1×4 + 0×2 + 1×1 = 13. As a 4-bit number, the 2's complement of 1101 is found by inverting to 0010 and adding 1 → 0011, representing −3.
Traps that cost marks
Applying De Morgan without swapping AND for OR; writing the NAND output as 1 when all inputs are 1; confusing BCD with pure binary; forgetting the carry-in in a full adder; and treating a flip-flop as combinational logic.