1.1 Data Representation in a Digital Computer

Digital computers store and process all information — numbers, text, images, sound — using only two symbols: 0 and 1. This section explains why binary is used and how data is organized in a digital system.

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Why Binary?

A digital computer is built from millions of tiny electronic switches called transistors. Each transistor has exactly two stable states:

Because hardware can reliably distinguish between only two voltage levels, the binary number system (base-2) is the natural choice for representing data. Using more than two levels would make circuits far more complex and error-prone.

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Units of Data

Bit

A bit (binary digit) is the most fundamental unit of data. It holds a single value: either 0 or 1.

Nibble

A nibble is a group of 4 bits. It can represent $2^4=16$ different values (0–15).

Byte

A byte is a group of 8 bits. It can represent $2^8=256$ different values and is typically used to store a single character.

Larger Units

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Character Encoding

To represent text, computers use character encoding schemes that map characters to binary numbers.

ASCII

ASCII (American Standard Code for Information Interchange) is the most widely used encoding for English text.

• Standard ASCII: uses 7 bits → $2^7=128$ characters (letters A–Z, a–z, digits 0–9, punctuation, control characters)
• Extended ASCII: uses 8 bits → $2^8=256$ characters (adds special symbols and accented letters)

Example:

• The letter A = ASCII code 65 = binary 01000001
• The letter a = ASCII code 97 = binary 01100001

Unicode

Unicode is a universal encoding standard designed to represent all written languages in the world.

• Assigns a unique code point to every character in every language (Latin, Arabic, Chinese, Urdu, emoji, etc.)
• The most common implementation is UTF-8, which uses 1–4 bytes per character
• Backward compatible with ASCII for the first 128 characters

EBCDIC

EBCDIC (Extended Binary Coded Decimal Interchange Code) is an 8-bit encoding used primarily on IBM mainframe computers. It is not commonly used in modern personal computers.

BCD (Binary Coded Decimal)

BCD represents each decimal digit (0–9) using a 4-bit binary code. It is used in applications where decimal accuracy is critical, such as financial calculations and digital clocks.

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Summary Table

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