Binary and denary

5 minAS Level1.1.2

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can convert any whole number between binary and denary, both ways, without a calculator.

Same idea, different base

You already use a place value system. In denary (base 10) each digit is 0 to 9, and the columns are worth 1, 10, 100, 1000, each ten times the one to its right.

Binary (base 2) works exactly the same way with only two digits, 0 and 1. So each column is worth double the one to its right: 1, 2, 4, 8, 16, 32, 64, 128 …

Definition

Number base

The number of different digits a place value system uses. Each column is worth the base times the column to its right. Denary is base 10 (digits 0 to 9); binary is base 2 (digits 0 and 1).

Binary to denary: add up the column values wherever there's a 1.

Worked example: Binary to denary

Convert 0110 1101 to denary.

Have a go first?

Quick check

CalculateQuestion 1 · Recall

One-line answerQuestion 2 · Recall

Answer the 2 questions above to continue.