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Year 8 · Spring 1 · Representations: from clay to silicon

Units and an introduction to hexadecimal

TheoryPresent ▶

What this lesson covers

Topic 2 Bits and bytes

KS3 Computing · A bit is one switch: 0 or 1. A byte is 8 bits. Every photo, song and game is measured by counting these.

Topic 3 Binary, denary and hex

KS3 Computing · They're three ways of writing the same numbers. Each one uses place value; only the number of digits changes.

Computer SystemsCambridge Lower Secondary Computing 0860

You will learn to

  • Convert between bits, bytes, KB, MB and GB, using × 8 and × 1000.
  • Explain why one hex digit stands for exactly four bits, called a nibble.
  • Convert a byte to two hex digits by splitting it into two nibbles.
  • Explain that a colour code like #FF8800 is three bytes: red, green and blue.

Success criteria

  • I can convert 3 MB to bytes and to bits.
  • I can convert 10011100 to 9C, and 9C back to binary.
  • I can read #FF8800 as red 255, green 136 and blue 0.

Key words

Say each word, then read what it means. Every one is in the glossary too.

Hexadecimal
Base 16: digits 0–9 then A–F. One digit = 4 bits.
Bit
One binary digit, 0 or 1. One switch.
Byte
8 bits. 256 possible patterns.
Nibble
4 bits. One hex digit.
Denary
Base 10. Our everyday numbers.
Binary
Base 2. Digits 0 and 1. Columns 128 64 32 16 8 4 2 1.
Overflow
A result too big for the bits available.

The explanation

Read it here, or open the study page below to go one step at a time with things to try.

Converting between units

★Remember

Going to a bigger unit: divide. Going to a smaller unit: multiply.

?Why?

Why? Think of money. 3 euros = 300 cents. Cents are smaller, so you need more of them. More = bigger number = multiply.

e.g.Example

3 MB → bytes: 3 × 1000 = 3,000 KB. Then 3,000 × 1000 = 3,000,000 bytes. Then × 8 = 24,000,000 bits.

Hexadecimal: why it exists

Binary is hard for people to read: 1001110011110101. Hexadecimal is a shorthand.

?Why?

Why 16? 4 bits make 16 patterns (2⁴ = 16). So one hex digit = exactly 4 bits. One byte = exactly 2 hex digits.

Denary101112131415
HexABCDEF
!Watch out

Hex doesn't change how the computer stores anything. It's only a way for humans to write binary.

Converting with hex

  • Binary → hex: split into groups of 4. 1001 | 1100 → 9 | 12 → 9C.
  • Hex → binary: each digit becomes 4 bits. 3F → 0011 1111.
  • Hex → denary: first digit × 16, plus second digit. 9C = 9 × 16 + 12 = 156.
  • Denary → hex: divide by 16. 200 ÷ 16 = 12 remainder 8 → C8.
e.g.Example

Web colours are hex: #FF0000 is pure red.

Study it

Open the study page and go one step at a time.

Topic 3 · Year 8

Binary, denary and hex

Computers store numbers in binary (base 2). We use denary (base 10). Programmers use hex (base 16) as a short way to write binary. All three use place value.

Topic 2 · Year 7

Bits and bytes

A bit is one switch: 0 or 1. A byte is 8 bits. Every file is measured by counting these.

The steps for this lesson

Check yourself

One question at a time. The reason shows after each answer.

Saved on this device.