Knowledge/A Level/H446/01 Computer systems/Boolean Algebra/Using logic gate diagrams and truth tables

Using logic gate diagrams and truth tables

Using logic gate diagrams and truth tables. See appendix 5d

1.4.3 Boolean Algebra

Boolean Algebra — Note 4 of 5

Candidates should be able to construct logic gate diagrams from a Boolean expression and vice-versa. Candidates should be able to construct truth tables from Boolean expressions and logic gate diagrams.

What you need to know

Logic gate diagrams represent Boolean expressions as circuits, and truth tables show the output for every possible combination of inputs. You need to convert between expressions, diagrams and truth tables in every direction.

What to know

Gates to know: AND, OR, NOT and XOR, drawn with the standard symbols from appendix 5d.
A truth table with n inputs has 2^n rows.
To build a truth table from an expression, add a column for each intermediate part of the expression, then the final output.
To draw a circuit from an expression, start with the innermost brackets and work outwards, one gate per operator.
To write an expression from a circuit, label the output of each gate as you work from inputs to the final output.

Exam technique

Tip:Draw the correct gate SHAPES. Labelling a box with 'AND' is not accepted.
Mistake:Forgetting the circle on a NOT gate, or giving an AND/OR gate more than two inputs when the question expects two.

Boolean Algebra

Note 4 of 5

1Define problems using Boolean logic
2Manipulate Boolean expressions, including the use of Karnaugh maps
3De Morgan's Laws, distribution, association, commutation and double negation
4Using logic gate diagrams and truth tables
5The logic associated with D type flip flops, half and full adders

Topic overview

← Previous noteDe Morgan's Laws, distribution, association, commutation and double negation1.4.3 Boolean Algebra Next note →The logic associated with D type flip flops, half and full adders1.4.3 Boolean Algebra

Back to Boolean Algebra