Digital Electronics and Logic Families
This domain tests number systems, Boolean algebra, gate-level simplification and the electrical comparison of TTL and CMOS families.
Core concepts
- Conversions between binary, octal, hex and BCD. BCD codes each decimal digit separately; it is not the same as binary.
- Universal gates: NAND and NOR can build any function. De Morgan: (A·B)' = A' + B' and (A + B)' = A'·B'.
- Useful identities: A + A'B = A + B; A + AB = A; A·A' = 0; A + A' = 1.
- Logic families: TTL uses bipolar transistors, 5 V supply, higher power, moderate speed, output high near 2.4 V minimum. CMOS uses MOSFETs, wide supply range, very low static power, but unused inputs must never float because that causes oscillation and excess current.
- Comparison parameters: fan-out (driven inputs), noise margin (V_IH − V_OH and V_IL − V_OL), propagation delay, power dissipation, power–delay product, and speed–power product trade-offs.
Worked example
Simplify F = AB + A(B + C) + B(B + C). Expand: AB + AB + AC + B + BC = AB + AC + B + BC. Factor B: B(A + 1 + C) + AC. Since 1 + A + C = 1, F = B + AC. The truth-table check at A = 1, B = 0, C = 1 gives AC = 1, so F = 1, matching the original expression.
Traps
Writing A + A'B as A + B is correct, but A·(A' + B) = AB, not A; forgetting to invert after applying De Morgan; treating BCD 1001 as nine in binary arithmetic without correction; leaving CMOS inputs floating.