Logic Circuits
Identification of common logic gate symbols, tables and equivalent circuits; applications used in aircraft systems and schematic diagrams; Boolean algebra, De Morgan's theorems and combinational arithmetic circuits.
Logic circuits, summary notes
- The seven standard gates are AND (all inputs high), OR (any input high), NOT/inverter, NAND (AND then invert), NOR (OR then invert), XOR (output high when inputs DIFFER) and XNOR (output high when inputs are the SAME).
- A truth table lists every input combination and the resulting output, n inputs give 2ⁿ rows.
- NAND and NOR are the universal gates: either one alone can be wired to produce any other function, which is why real ICs and gate arrays are built predominantly from them.
- De Morgan's theorems convert between AND and OR forms: break the bar and change the sign. (A·B)‾ = A‾ + B‾ and (A + B)‾ = A‾ · B‾.
- Boolean identities that simplify circuits: A·0 = 0, A·1 = A, A+0 = A, A+1 = 1, A·A‾ = 0, A+A‾ = 1, A·A = A, A+A = A.
- Combinational logic (gates, adders, encoders, decoders, comparators) has an output that depends only on the present inputs; sequential logic (flip-flops, counters, registers) also depends on previous state and needs a clock.
- A half adder sums two bits and produces SUM (XOR) and CARRY (AND). A full adder adds a carry-in as well, so full adders cascade to add multi-bit words.
- ⚠ Exam trap: XOR is not OR, with both inputs high, OR gives 1 but XOR gives 0. And a bubble on a symbol always means inversion at that point.
- De Morgan (NAND)
- (A·B)‾ = A‾ + B‾
- De Morgan (NOR)
- (A + B)‾ = A‾ · B‾
- Boolean identities
- A·0 = 0 · A·1 = A · A+0 = A · A+1 = 1 · A·A‾ = 0 · A+A‾ = 1
- Truth-table size
- rows = 2ⁿ for n inputs
- Half adder
- SUM = A ⊕ B · CARRY = A · B
Simplify (A·B)‾ and state the practical meaning.
By De Morgan, (A·B)‾ = A‾ + B‾. A NAND gate therefore behaves exactly like an OR gate fed with both inputs inverted, the standard "bubbled OR" equivalent symbol on schematics.
A landing-gear warning must sound when the gear is NOT down AND the throttle is closed. Which single gate implements this from a "gear down" signal and a "throttle closed" signal?
Invert "gear down" and AND it with "throttle closed", an AND gate with one inverted (bubbled) input, which is the same as a NOR of "gear down" and "throttle not closed". The output is high only when the gear is up and the throttle is closed.
Logic gate playground
Half adder & full adder
Logic circuits concept map
Logic Circuits
Logic circuits quiz
Logic Circuits, quiz
1. The gate symbol shown has a flat back and a rounded output end. Its output Q is high only when:
Both A and B are highEither A or B is highBoth A and B are low2. The gate symbol shown has a curved back and a pointed output. Its output Q is high when:
Either or both inputs are highBoth inputs are high onlyBoth inputs are low3. The gate shown has a flat back, a rounded end and a small circle on its output. That circle indicates:
The output is invertedThe output is delayedThe input is inverted4. The gate shown has a double curved back. Its output is high when:
The inputs are differentThe inputs are the sameBoth inputs are high5. In the circuit shown, an AND gate feeds one input of an OR gate. The output Q is high when:
A and B are both high, or C is highA, B and C are all highOnly when C is low6. The circuit shown, an exclusive OR gate and an AND gate sharing the same two inputs, is a:
Half adderFull adderDecoder7. The output of a 2-input AND gate is HIGH only when:
Both inputs are HIGHAny input is HIGHBoth inputs are LOW8. Which pair of gates are "universal"?
NAND and NORAND and ORXOR and XNOR9. (A + B)‾ is equivalent to:
A‾ · B‾A‾ + B‾A · B10. (A · B)‾ is equivalent to:
A‾ + B‾A‾ · B‾A + B11. A 2-input XOR gate gives a HIGH output when the inputs are:
DifferentBoth HIGHBoth LOW12. A NAND gate is equivalent to:
AND followed by NOTOR followed by NOTTwo NOT gates13. A truth table for a 3-input gate has how many rows?
86314. In Boolean algebra, A + 1 equals:
1A0