Logic Gates and Truth Tables

Overview

Recall questions on truth tables, the AND, OR, NOT, XOR, NAND and NOR gates with their symbols and tables, reading and drawing gate diagrams, writing expressions from circuits, and proving equivalence with a truth table.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   What is a truth table, and how many rows does one need?

   Model answer

   A table listing every possible combination of the input values to a logic circuit or expression, with the resulting output for each. Because each input is either 0 or 1, a circuit with n inputs needs 2 to the power n rows: 4 rows for two inputs, 8 for three, 16 for four. The input columns are normally written in ascending binary order so that no combination is missed.

2. 2

   Describe the AND gate: its symbol, its behaviour and how the operation is written.

   Model answer

   The symbol is a shape with a flat left edge and a semicircular right edge, like a capital D, with the inputs entering on the left and the single output leaving from the curved right side. The output is 1 only when every input is 1, and 0 otherwise. Common ways of writing it are A.B, AB, A AND B and A and B joined by a wedge; several notations are accepted, so use whichever you are comfortable with as long as it is unambiguous.

3. 3

   Give the truth table for a two-input AND gate.

   Model answer

   With inputs A and B: 0 and 0 give 0; 0 and 1 give 0; 1 and 0 give 0; 1 and 1 give 1. Only the last row produces a 1.

4. 4

   Describe the OR gate and give its truth table.

   Model answer

   The symbol is a shield or arrowhead shape: a curved left edge that the inputs pass through, with the two upper and lower edges sweeping to a point on the right where the output leaves. The output is 1 when at least one input is 1. Truth table: 0,0 gives 0; 0,1 gives 1; 1,0 gives 1; 1,1 gives 1. It is usually written A+B, A OR B, or with a vee between the terms.

5. 5

   Describe the NOT gate and give its truth table.

   Model answer

   The symbol is a small triangle pointing right with a circle (a bubble) on its tip, with one input on the left and one output on the right. It inverts its single input: an input of 0 gives an output of 1, and an input of 1 gives an output of 0. It may be written as A with a bar over it, as A', or as a not-sign in front of A - all are accepted.

6. 6

   Describe the XOR gate and give its truth table.

   Model answer

   The symbol is the OR shape with an additional curved line drawn just outside and parallel to its curved left edge. Exclusive OR gives an output of 1 when the inputs are different and 0 when they are the same. Truth table: 0,0 gives 0; 0,1 gives 1; 1,0 gives 1; 1,1 gives 0. It is written with a plus sign inside a circle, or as A XOR B.

Other ways to work this

The same content, four other ways.

What is inside Levo

Six ways to work the same material.