Binary numbers

Summary

Binary is a way to write numbers using only 0 and 1. Each position stands for a power of two, so 10110₂ means 16 + 4 + 2, which is decimal 22.

Introduction

You already use place values in decimal: the digits in 347 mean three hundreds, four tens, and seven ones. Binary follows the same idea, but its places are ones, twos, fours, eights, and so on.

Explanation

Write the place values from right to left: 1, 2, 4, 8, 16, .... A 1 means “include this value”; a 0 means “do not include it.” To turn a decimal number into binary, first choose the largest place value that does not exceed the number. Subtract it, then repeat with smaller places.

Real-world example

Read every column

To turn 22 into binary, start with 16. It fits, leaving 6. Next, 8 does not fit, so write 0. Then 4 fits, leaving 2; 2 fits, leaving 0; and 1 does not fit. The included places make 10110.

Code example

const decimal = 22;
console.log(decimal.toString(2)); // 10110
console.log(Number.parseInt('10110', 2)); // 22

Common mistakes

• Reading 10110 as “ten thousand one hundred ten”; it is not decimal.
• Starting binary place values at two instead of one.
• Treating the base marker in 10110₂ as another digit.

Quiz

Key takeaways

• Binary positions are powers of two.
• A 1 includes a place value and a 0 excludes it.
• Conversion works in both directions using place values.