Logic gates, logic circuits and Boolean algebra

Learning objectives

Draw and recognise the standard symbols for the NOT, AND, OR, NAND, NOR and XOR gates and write the truth table for each one

Construct a logic circuit from a written problem statement or from a Boolean expression, and complete the truth table for a circuit with up to three inputs

Write the Boolean expression produced by a given logic circuit, and draw the logic circuit described by a given Boolean expression

(A Level) Simplify a Boolean expression using the commutative, associative, distributive, absorption and De Morgan laws, and confirm the simplification with a truth table

(A Level) Complete a Karnaugh map from a truth table or a sum-of-products expression, group the ones to read off a simplified expression, and explain why groups must be rectangular blocks whose size is a power of two

(A Level) Describe the behaviour of the SR and JK flip-flops built from NAND gates, and explain how a flip-flop is used to hold a single bit of data

Recognise that circuits with the same truth table are equivalent, and that the same outputs can often be produced with fewer gates

(A Level) Produce the truth tables, Boolean expressions and circuits of a half adder and a full adder, including gates with more than two inputs, and explain how full adders are chained to add multi-bit numbers