IB Computing: 4.2 Boolean logic

Boolean Logic

4.2 Boolean logic

Presumably the 3 inputs is to a circuit but the circuit could consist of, say, just one gate, theoretically.

On this page: [ basics | truth tables | expressions ]

Basic Gates

Candidates need to know the basic operators and, or, not, nand, nor and xor, their symbols , how to express them in conventional notation and their truth tables (with a maximum of three inputs).

Boolean expressions can also be written in words:

(A xor not B)

Truth Tables

and			or			not
A	B	A and B	A	B	A or B	A	not A
0	0	0	0	0	0	0	1
0	1	0	0	1	1	1	0
1	0	0	0	1	1
1	1	1	1	1	1

nand			nor			xor
A	B	A nand B	A	B	A nor B	A	B	A xor B
0	0	1	0	0	1	0	0	0
0	1	1	0	1	0	0	1	1
1	0	1	1	0	0	1	0	1
1	1	0	1	1	0	1	1	0

Boolean expressions

You can be asked to construct Boolean expressions using the above operators, for example:

This expression is equivalent to (A xor not B) and (C nor D).

The value of a Boolean expression such as can be given in a truth table:

Input	Input	intermediate	Output
a	b	*not* b	a xor not* b*
0	0	1	1
0	1	0	0
1	0	1	0
1	1	0	1

Complete the truth table for

Input	Input	Output
c	d	c nor* d*

Complete the truth table for the whole expression

Input	Input	Input	Input			Output
a	b	c	d	a xor* not b*	c nor* d*	(a xor* not b) and (c nor d)*

related: [ Topic 4 home | next: Simplifying Boolean expressions ]

About logic symbols, operators and truth tables.

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