Why Do Computers Use Binary?
At the heart of every computer are billions of tiny electronic switches called transistors. Each transistor has exactly two states: it is either on (current flowing through it) or off (no current). There is no in-between.
This physical reality shapes everything about how computers store and process data. Because a transistor can only be in one of two states, computers use a number system with exactly two digits — 0 (off) and 1 (on). This is called the binary number system, or base-2.
Every piece of information inside a computer — text, images, music, programs — is ultimately stored as a long sequence of 0s and 1s. Understanding binary is therefore understanding the most fundamental language of computing.
Counting in Binary
The everyday number system we use is base-10 (decimal). It uses ten digits (0–9), and each position in a number represents a power of 10:
Decimal 345 = (3 × 100) + (4 × 10) + (5 × 1)
= (3 × 10²) + (4 × 10¹) + (5 × 10⁰)
Binary works the same way, but each position represents a power of 2 instead:
| Position | 2^7 | 2^6 | 2^5 | 2^4 | 2^3 | 2^2 | 2^1 | 2^0 |
|---|---|---|---|---|---|---|---|---|
| Value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
In binary you can only place a 0 or a 1 in each position. Here is how you count from 0 to 7 in binary:
| Decimal | Binary |
|---|---|
| 0 | 000 |
| 1 | 001 |
| 2 | 010 |
| 3 | 011 |
| 4 | 100 |
| 5 | 101 |
| 6 | 110 |
| 7 | 111 |
Once all digits are 1, you need an extra digit to go higher — just as decimal goes from 9 to 10.
With 3 binary digits (bits) you can represent 8 different values (0 to 7). With 4 bits you can represent 16 values (0 to 15). In general, n bits can represent 2 to the power of n distinct values.
Converting Binary to Decimal
To convert a binary number to decimal, write out the place values and add up the positions where there is a 1.
Example: convert 1011 to decimal
Position values: 8 4 2 1
Binary digits: 1 0 1 1
= (1 × 8) + (0 × 4) + (1 × 2) + (1 × 1)
= 8 + 0 + 2 + 1
= 11
So binary 1011 equals decimal 11.
Example: convert 10110 to decimal
Position values: 16 8 4 2 1
Binary digits: 1 0 1 1 0
= 16 + 0 + 4 + 2 + 0
= 22
Converting Decimal to Binary
To convert decimal to binary, repeatedly divide by 2 and record the remainders, then read the remainders from bottom to top.
Example: convert decimal 13 to binary
13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Reading remainders bottom to top: 1101
Check: 8 + 4 + 0 + 1 = 13. Correct.
When converting to binary, work from the largest power of 2 that fits. For 25: does 16 fit? Yes (25 - 16 = 9). Does 8 fit into 9? Yes (9 - 8 = 1). Does 4 fit into 1? No. Does 2 fit into 1? No. Does 1 fit? Yes. Result: 11001.
Bits, Bytes, and Beyond
A single binary digit is called a bit (binary digit). Bits are the smallest possible unit of information.
Because a single bit can only hold a 0 or a 1, real data is stored in groups:
| Unit | Size | What it can store |
|---|---|---|
| Bit | 1 bit | A single 0 or 1 |
| Byte | 8 bits | One character (e.g. the letter "A") |
| Kilobyte (KB) | 1 024 bytes | A short text document |
| Megabyte (MB) | 1 024 KB | A medium-resolution photo |
| Gigabyte (GB) | 1 024 MB | A full-length HD film |
A byte (8 bits) is the standard unit for measuring file sizes and storage capacity. With 8 bits, 256 different values can be represented (from 0 to 255), which is enough to encode every letter, digit, and common punctuation mark in the ASCII character set.
The letter "A" is stored as the binary value 01000001 (decimal 65). Every character on your keyboard has its own agreed-upon binary code. When you type a message, the computer is working with sequences of these 8-bit values the entire time.
Binary in Everyday Computing
Binary is not just an abstract concept — it is present in everything your computer does:
- Colours on screen are stored as three bytes (red, green, blue), each 0–255.
- Sound is stored as millions of binary measurements per second.
- Programs are stored as binary instructions the CPU executes directly.
Learning binary gives you the foundation to understand how computers handle memory addressing, networking, encryption, and much more.
Practice Problems
Convert binary 1100 to decimal.
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Convert decimal 9 to binary.
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How many different values can 4 bits represent?
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How many bytes are in a kilobyte?