Expressions and circuits with two and three inputs, truth tables with working columns, and writing the expression for a circuit.
What you will learn
- Work out the output of an expression or circuit
- Complete truth tables with a working column
- Write the expression for a circuit or truth table
- Simplify simple expressions
Expressions and circuits
A circuit joins gates: one gate's output becomes another's input.
An expression describes the same thing in writing.
- Q = (A AND B) OR NOT C
- Work out the brackets first: A AND B.
- Then NOT C.
- Then OR the two results.
Without brackets, NOT is done first, then AND, then OR (just as × comes before + in maths). Questions usually add brackets to make the order clear.
For a three-input truth table, add a working column for each bracket. It saves mistakes.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Expressions and circuits
- Build it yourself
- From circuit to expression
- Equivalent and simpler expressions
- Try it: Follow the inputs through
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
Expression, Working column, Equivalent
In this unit: Boolean logic
AND, OR, NOT and XOR gates, truth tables, expressions and circuits, built by hand in an interactive gate builder and used to describe real systems.
- Logic gates and truth tables
- Combining gates
- Logic for real systems