Binary Code: How Computers Represent Numbers and Letters

What is binary code?

Binary code is a way of writing data using only two symbols, 0 and 1. Each symbol is one bit; groups of bits stand for numbers, letters, or instructions that a computer can store and process.

Two symbols are enough because a circuit only has to tell two states apart, and telling two apart is far more reliable than telling ten apart. Everything above that — numbers, letters, pictures, sound — is a matter of agreeing what a group of bits stands for.

What do the 0 and 1 in binary code mean?

Each 0 or 1 is a bit: a switch that is off or on. A bit alone holds two values; 8 bits (one byte) hold 256 combinations, enough for every letter, digit and symbol in ASCII.

A byte is 8 bits and holds 256 values, 0–255; a nibble is 4 bits.

Each extra bit doubles the count, so width is the only thing that limits what a group can hold. how a bit, a nibble and a byte relate covers the units in depth.

How does binary code represent a letter?

A letter is stored as its character code written in 8 bits. The letter A has ASCII code 65, and 65 in binary is 01000001, so A in binary code is 01000001.

The same row answers in any base: 'A' is 65 in decimal, 41 in hex, 101 in octal and 01000001 in binary. This page shows one row; every ASCII code and its character carries all 128.

What is the binary alphabet (A–Z in binary)?

The binary alphabet is the list of 8-bit codes for A–Z (01000001 to 01011010) and a–z (01100001 to 01111010). Lowercase letters differ from uppercase by one bit, worth 32.

A is ASCII 65 = 0x41 = 0o101 = 0b01000001; a is 97 = 0x61 = 0o141 = 0b01100001. Uppercase and lowercase differ by 32, which is bit 5.

How do you write words in binary code?

Write each character's 8-bit code in order and separate the bytes with spaces: "Hi" is 01001000 01101001. Spaces and punctuation have codes too, so a whole sentence can be written the same way.

Result: Hi = 01001000 01101001

The same two characters answer in every base: 'Hi' is 72 105 in decimal, 48 69 in hex, 110 151 in octal and 01001000 01101001 in binary. To do it for a whole message, convert a message into binary code.

How do you read binary code?

Split the string into 8-bit groups, turn each group into its decimal value, and look that value up in the ASCII table: 01001000 is 72, and 72 is H. A converter does the lookup for you.

The grouping matters more than the digits. Drop one bit and every group after it shifts, so a line that decodes into nonsense is usually a spacing problem rather than a value problem. The binary translator for 8-bit groups does the splitting and the lookup in one pass.

Which character code does binary code use, ASCII or UTF-8?

Plain English text uses ASCII codes 0–127, one byte each. UTF-8 keeps those bytes and adds two to four bytes for other characters, so é is 11000011 10101001. Most tools default to UTF-8.

ASCII defines 128 characters, codes 0–127, using 7 bits; in practice each code is stored in one 8-bit byte with a leading 0.

UTF-8 encodes each character in 1 to 4 bytes. Characters 0–127 use one byte identical to ASCII, so ASCII text is valid UTF-8.

é is U+00E9 and encodes as C3 A9 (2 bytes); € is U+20AC and encodes as E2 82 AC (3 bytes); 😀 is U+1F600 and encodes as F0 9F 98 80 (4 bytes).

é is the shortest of those three examples: the code point is 233, and the two UTF-8 bytes are hex C3 A9, octal 303 251 and binary 11000011 10101001. Two groups, one character — which is where a byte count and a character count stop agreeing. where UTF-8 takes over from ASCII has the rest of the rule.

What is the difference between binary code and the binary number system?

The binary number system is base 2: 1010 means the number ten. Binary code uses the same digits to label things, so 01000001 can mean the number 65 or the letter A depending on the code in use.

The number system has place value: each position is worth twice the one to its right, and the digits are added up. A code has no arithmetic in it at all — the value is looked up in a table that somebody agreed on.

One hexadecimal digit equals exactly 4 bits (16 = 2⁴); one octal digit equals exactly 3 bits (8 = 2³). Hex and octal are therefore converted by grouping bits, and hex ↔ octal passes through binary.

That grouping is why binary, octal and hex are three views of one bit string. Decimal has no such shortcut; repeated division and positional expansion are the two routes between any pair of bases.

Is binary a language?

Binary is a code, not a language: it has no grammar or vocabulary of its own. "Binary language" usually means machine code, the binary instructions a processor runs, or plain text written in binary.

The distinction matters when someone asks for a translation. A phrase can be written in binary, and the result is the same phrase in a different notation — not a second phrase that means the same thing.

Where is binary code used?

Every file a computer stores is binary: text as character codes, images as pixel values, sound as samples, programs as machine instructions. Networks send the same bits over wires and radio.

• Text — one character code per character, 8 bits at a time.
• Images — a value per colour channel per pixel.
• Sound — a sample of the waveform thousands of times a second.
• Programs — machine instructions the processor decodes directly.

Who invented binary code?

Gottfried Leibniz described the binary number system in 1679; Francis Bacon's 1605 cipher used two symbols for letters; the ASCII code that maps letters to 8-bit binary was published in 1963.

The two halves arrived separately: a way of counting in twos, and an agreement about which number stands for which character. Computing needed both, and only the second one had to be negotiated.