Chapter10 - Boolean Logic

3.01 Logic Gates

Key Terms

Logic gate - the basic foundation of a digital circuit that controls the flow of electronic signals.
Digital circuit - a circuit where electronic signals are one of two values, high voltage (l) or low voltage (0).
Voltage - the potential difference across an electrical component needed to make electricity flow through it.
Microprocessor - an integrated circuit that provides the same functions of a CPU.
Truth table - a way of showing every outcome of a logic gate.

Logic Gates

NOT Gate
AND Gate

OR Gate
NAND Gate (NOT AND)

NOR Gate (NOT OR)
XOR Gate (XOR Gate)

. represents the AND operation
+ represents the OR operation
a bar (above the letter or letters, e.g. a) represents the NOT operation.

Logic circuits, logic expressions, truth tables and problem statements

Type 1 - produce a truth table for a given logic circuit

题目：找出对应逻辑图(logic circuit)的真值表(truth table)

Step 1 - find the intermediate values P and Q

找出对应逻辑图(logic circuit)的真值表(truth table)

Step 2 - find intermediate values R use P and Q

找出对应逻辑图(logic circuit)的真值表(truth table)

Step 3 - find final part X use intermediate R and C

找出对应逻辑图(logic circuit)的真值表(truth table)

Final result

找出对应逻辑图(logic circuit)的真值表(truth table)

Type 2 - write logic expressions from given logic circuits

Example 1

logic gate1:: (A AND B)
logic gate2:: (B OR C)
final result:: (A AND B) XOR (B OR C)

Example 2

logic gate 1:: (A NAND C)
logic gate 2:: (B AND C)
logic gate 3:: (logic gate 1) NOR A ~ ((A NAND C) NOR A)
logic gate 4:: ((A NAND C) NOR A) OR (B AND C)

Type 3 - produce a logic circuit and a truth table from given logic expression

Example 1

Given logic expression: (A XOR C) OR (NOT C NAND B)

first step - A XOR C

second step - NOT C NAND B

third step - combine

fourth step - truth table

Type 4 - produce a logic expression and logic circuit from given truth table (optional)

Example 1

logic circuit

Example 2

logic circuit

Example 3

(NOT A AND NOT B AND NOT C) 
(A AND NOT B AND NOT C) 
(A AND B AND NOT C)

final logic expression

(NOT A AND NOT B AND NOT C) 
OR (A AND NOT B AND NOT C) 
OR (A AND B AND NOT C)

Type 4 - Produce a logic circuit and truth table from real work case

example 1

A safety system uses three inputs to a logic circuit. An alarm, X, sounds if input A represents ON and input B represents OFF; or if input B represents ON and input C represents OFF.