The bit: one switch, one answer
Inside a computer there are billions of tiny switches. Each switch is either off or on. We write off as 0 and on as 1. One switch is called one bit.
Where the name comes from. Binary digit → bit. Binary means "made of two".
One bit = one yes/no answer. Is the light on? Is the box ticked? Is the pixel black? Each of those needs exactly one bit.
One bit alone is not much. It can only say two things. To store anything bigger, a computer uses lots of bits side by side, and reads them as one pattern.
Find my number with yes/no questions
I'm thinking of a number from 0 to 15. Each question halves what's left. Every answer is one bit: yes = 1, no = 0.
Why did it always take exactly 4 questions? 16 numbers. Each yes/no answer cuts the list in half: 16 → 8 → 4 → 2 → 1. Four halvings, so four answers, so 4 bits. Your four answers, read left to right, are the number written in binary.
More bits = more patterns
Put bits side by side and read them together. Each extra bit doubles the number of different patterns you can make.
| Bits | Every pattern | How many | As a sum |
|---|---|---|---|
| 1 | 0, 1 | 2 | 2 |
| 2 | 00, 01, 10, 11 | 4 | 2 × 2 |
| 3 | 000 … 111 | 8 | 2 × 2 × 2 |
| 4 | 0000 … 1111 | 16 | 2 × 2 × 2 × 2 |
| 8 | 00000000 … 11111111 | 256 | 2 multiplied by itself 8 times |
Why multiply, not add? Every pattern you already had can be followed by a 0 or a 1. Each old pattern becomes two new ones. "Each one becomes two" is what × 2 means.
An old games console used 16-bit colour: 2¹⁶ = 65,536 colours. Modern screens use 24 bits: 2²⁴ = 16,777,216 colours. 8 more bits made 256 times as many.
The biggest number n bits can hold
If bits store a whole number, the smallest is 0 (all zeros). The biggest is all ones. But it is one less than the number of patterns. Here's why.
3 bits make 2³ = 8 patterns.
Give each pattern a number, starting at 0: 000 = 0, 001 = 1 …
Zero takes one of the 8 patterns. That leaves 7 patterns for 1, 2, 3, 4, 5, 6, 7.
So the biggest is 8 − 1 = 7, written 111.
Same for a byte: 2⁸ = 256 patterns, so it counts from 0 to 255.
"How many values?" → 2ⁿ (256 for a byte). "What is the biggest value?" → 2ⁿ − 1 (255). Read the question twice: they are different numbers.
The byte: why 8 bits?
A byte is 8 bits. Nobody was forced to pick 8. People chose it, and it won for four good reasons.
It fits one letter. English text needs about 100 symbols (A–Z, a–z, 0–9, punctuation). 7 bits give 128 patterns; 8 bits give 256, with room to spare.
8 is a power of 2. 8 = 2 × 2 × 2. Computers count in twos, so 8 joins into 16, 32, 64 cleanly.
It splits exactly in half. Two groups of 4 bits. A group of 4 is a nibble, and one nibble is exactly one hexadecimal digit (Year 8).
IBM made it the standard. IBM's System/360 computers (1964) used 8-bit bytes. They sold so well that everyone else followed.
Werner Buchholz at IBM made up the word in 1956: a "bite-sized" chunk of bits. He spelt it with a y so nobody would misread it as "bit".
Bigger units: the ladder
Files are huge, so we group bytes into bigger units, like grams and kilograms. Each rung of the ladder is 1,000 times the one below it.
Climb the ladder
Going to a smaller unit: multiply (you need more of them). Going to a bigger unit: divide. Bytes → bits is always × 8, not × 1000.
Why multiply when going down? Money: 3 euros = 300 cents. Cents are smaller, so you need more of them to make the same amount. More = bigger number = multiply.
1000 or 1024?
There are two rulers. Kilo means 1,000 (like a kilometre). But computers count in powers of 2, and the nearest power of 2 to 1,000 is 2¹⁰ = 1,024. In 1998 the 1,024 versions got their own names: kibibyte (KiB), mebibyte (MiB), gibibyte (GiB).
| Decimal (×1000) | Binary (×1024) | Difference |
|---|---|---|
| 1 KB = 1,000 bytes | 1 KiB = 1,024 bytes | 2.4% |
| 1 MB = 1,000,000 bytes | 1 MiB = 1,048,576 bytes | 4.9% |
| 1 GB = 1,000,000,000 bytes | 1 GiB = 1,073,741,824 bytes | 7.4% |
| 1 TB = 10¹² bytes | 1 TiB = 1,099,511,627,776 bytes | 10% |
Why does a "1 TB" drive show about 931 GB on Windows? The maker counts 1,000,000,000,000 bytes. Windows divides by 1,024 three times (≈ 931) but still writes "GB". Nothing is missing. Same amount, different ruler.
AQA expects both (kilo = 1000, kibi = 1024). OCR accepts either. 1000 is quicker by hand, so use it unless the question says otherwise.
Bits vs bytes in internet speeds
File sizes are counted in bytes (big B: MB). Internet speeds are counted in bits per second (small b: Mbps). One letter's case changes the number by 8.
Why do internet companies use bits? A network sends data one bit at a time down the wire, so bits per second is the natural measure for the wire. It also makes the number on the advert 8 times bigger.
A 4 GB game on 100 Mbps: 4,000 MB × 8 = 32,000 megabits. 32,000 ÷ 100 = 320 seconds, about 5 minutes 20 seconds at best.
A sense of scale
Knowing roughly how big things are lets you spot silly answers. If you work out a photo is 5 GB, something went wrong.
| Thing | Rough size |
|---|---|
| One letter in plain text | 1 byte |
| A page of plain text | about 2 KB |
| A phone photo | 2–5 MB |
| A 3-minute song (MP3) | 3–4 MB |
| An hour of HD video | 1–3 GB |
| A big modern game | 50–150 GB |
How many fit?
Common mix-ups
These are the mistakes almost everyone makes at first. Read the left side, then the right.
A byte is 10 bits, or 1,000 bits.
A byte is exactly 8 bits. Kilo = 1,000 is for the next step up.
8 bits can store numbers up to 256.
256 patterns, but 0 uses one, so the biggest is 255.
100 Mbps downloads 100 MB every second.
Speeds are in bits. 100 ÷ 8 = 12.5 MB per second at most.
Going KB → bytes you divide, because bytes are "smaller".
Smaller unit means you need more of them: multiply.
Adding 1 bit adds 1 more pattern.
Adding 1 bit doubles the patterns.
Check yourself
Quick questions first. Then endless practice: a wrong answer shows you the working, step by step.