Module 5.5 and 5.8 Logic circuits, encoders and decoders

Knowledge levels

Item	A	B3	B1	B2 / B2L
5.5(a) Logic gate symbols, truth tables, equivalent circuits, aircraft applications, schematics	—	—	2	2
5.5(b) Interpretation of logic diagrams	—	—	—	2
5.8 Encoders and decoders	—	—	—	2

Logic levels

Digital circuits use two states: 1 (true, high, e.g. +5 V or 28 V "ground/open" discretes) and 0 (false, low). In positive logic high = 1; in negative logic low = 1. Aircraft discrete signals are often "28 V/open" or "ground/open".

The basic gates

Gate	Boolean	Output is 1 when ...	Switch equivalent
AND	Q = A · B	all inputs are 1	switches in series
OR	Q = A + B	any input is 1	switches in parallel
NOT (inverter)	Q = Ā	input is 0	normally closed relay contact
NAND	Q = (A · B)‾	any input is 0	AND followed by NOT
NOR	Q = (A + B)‾	all inputs are 0	OR followed by NOT
XOR (exclusive OR)	Q = A ⊕ B	inputs are different	two-way (staircase) switch arrangement
XNOR	Q = (A ⊕ B)‾	inputs are the same	comparator / equality

Truth table (two inputs)

A	B	AND	OR	NAND	NOR	XOR	XNOR
0	0	0	0	1	1	0	1
0	1	0	1	1	0	1	0
1	0	0	1	1	0	1	0
1	1	1	1	0	0	0	1

Symbols

• Two symbol standards appear in manuals: distinctive-shape (ANSI/MIL: D-shape for AND, curved shield for OR, triangle for buffer) and rectangular (IEC: box with "&" for AND, "≥1" for OR, "=1" for XOR, "1" for buffer).
• A small circle (bubble) at an input or output means inversion.

Key fact: NAND and NOR are universal gates - any logic function can be built from NAND gates alone (or NOR gates alone).