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What Is Binary? Number Systems Explained
Published Apr 17, 2026
What Is Binary?
Binary (base-2) is the number system used internally by all modern computers. It uses only two digits: 0 and 1, corresponding to the two states of an electronic switch (off/on, low voltage/high voltage).
Every number, character, image, and instruction processed by a CPU is ultimately represented as a sequence of bits (binary digits).
The Four Common Number Bases
| Base | Name | Digits | Common use |
|---|---|---|---|
| 2 | Binary | 0–1 | CPU, memory, data storage |
| 8 | Octal | 0–7 | Unix file permissions (chmod 755) |
| 10 | Decimal | 0–9 | Everyday counting |
| 16 | Hexadecimal (hex) | 0–9, A–F | Memory addresses, colours, hash values |
How Positional Notation Works
Each position in a number represents a power of the base:
Decimal 2026:
2 × 10³ + 0 × 10² + 2 × 10¹ + 6 × 10⁰
= 2000 + 0 + 20 + 6 = 2026
Binary 11111101010 (= 2026 in decimal):
1×2¹⁰ + 1×2⁹ + 1×2⁸ + 1×2⁷ + 1×2⁶ + 1×2⁵ + 0×2⁴ + 1×2³ + 0×2² + 1×2¹ + 0×2⁰
= 1024 + 512 + 256 + 128 + 64 + 32 + 0 + 8 + 0 + 2 + 0 = 2026
Converting Decimal to Binary
Divide by 2 repeatedly, recording the remainder:
2026 ÷ 2 = 1013 r 0
1013 ÷ 2 = 506 r 1
506 ÷ 2 = 253 r 0
253 ÷ 2 = 126 r 1
126 ÷ 2 = 63 r 0
63 ÷ 2 = 31 r 1
31 ÷ 2 = 15 r 1
15 ÷ 2 = 7 r 1
7 ÷ 2 = 3 r 1
3 ÷ 2 = 1 r 1
1 ÷ 2 = 0 r 1
Read remainders from bottom to top: 11111101010
Hexadecimal — Compact Binary Representation
Each hex digit represents exactly 4 bits (a "nibble"), making it a convenient shorthand:
| Hex | Binary | Decimal |
|---|---|---|
| 0 | 0000 | 0 |
| 5 | 0101 | 5 |
| A | 1010 | 10 |
| F | 1111 | 15 |
Example: Hex #FF5733 (an orange-red colour):
FF = 1111 1111 = 255 (red channel)
57 = 0101 0111 = 87 (green channel)
33 = 0011 0011 = 51 (blue channel)
Octal and Unix Permissions
Unix file permissions are often shown in octal. Each digit represents three bits (read, write, execute):
chmod 755 → 7=111 (rwx), 5=101 (r-x), 5=101 (r-x)
Owner: read+write+execute
Group: read+execute
Others: read+execute
Bits, Bytes, and Beyond
| Unit | Bits |
|---|---|
| 1 bit | 1 |
| 1 nibble | 4 |
| 1 byte | 8 |
| 1 kilobyte (KB) | 8,192 |
| 1 megabyte (MB) | 8,388,608 |
Computers process data in multiples of 8 bits because 8 bits (one byte) can represent 256 values (0–255), which conveniently covers the ASCII character set, a colour channel value, and many protocol fields.
Use the Number Base Converter to convert any number between binary, octal, decimal, and hexadecimal.