---
title: "Binary Numbers and Place Value"
description: "Counting with two digits, where each column is worth twice the column to its right. Converting both ways between binary and decimal."
canonical: https://lightmysky.com/learn/computing/binary-numbers-and-place-value-mt_t67akIKBmI
source: https://lightmysky.com/learn/computing/binary-numbers-and-place-value-mt_t67akIKBmI.md
retrieved: 2026-09-12
---

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# Binary Numbers and Place Value

Counting with two digits, where each column is worth twice the column to its right. Converting both ways between binary and decimal.

Subject: Computing · Area: Computer Systems · Ages 14 to 15
Page: https://lightmysky.com/learn/computing/binary-numbers-and-place-value-mt_t67akIKBmI

## Ready when they can

- Convert an 8-bit binary number to decimal
- Convert a decimal number below 256 into 8 bits
- State the largest value 8 bits can hold, and why that is the limit

## Lesson: Two digits run the machine

You already met bits: wires that are either on or off, standing for 1 or 0. One such digit is the smallest piece of information a computer holds. Line several up in a row and the pattern can hold a number, the kind used to score a game or count your steps. Three wires can track three lightbulbs, one on-off choice each.

**Example.** Each column to the left is worth double: 1, 2, 4, 8, 16, and on. To read 1101, add the columns holding 1, which gives 8 + 4 + 1 = 13. Your turn: 37 is 32 + 4 + 1, written 100101.

To write a decimal number in binary, divide by 2 again and again and read the remainders upward. Eight bits make a byte, and a byte holds 0 to 255. That makes 255 the largest value 8 bits can hold, since 256 would need a ninth bit.

**Tip.** Write the place values above the digits and cross out the zeros. Then add only what is left.

**Recap.** Bits are on-off digits, columns double leftward, and 8 bits hold 0 to 255.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Powers of Ten Notation](https://lightmysky.com/learn/mathematics/powers-of-ten-notation-mt_bO-njVOige)
- [Data and Information for Computers](https://lightmysky.com/learn/computing/data-and-information-for-computers-mt_kH1DzOPsXG)
- [Why a Computer Works with Only Two Symbols](https://lightmysky.com/learn/computing/why-a-computer-works-with-only-two-symbols-mt_r0wLIjpi5R)

## Opens up

- [Adding Binary Numbers and Overflow](https://lightmysky.com/learn/computing/adding-binary-numbers-and-overflow-mt_dBS2OoQscq)
- [IP Addressing and How Routers Choose a Path](https://lightmysky.com/learn/computing/ip-addressing-and-how-routers-choose-a-path-mt_l0dRGocXGw)