[1.1.1] Binary represents all data

Why Computers Use Binary

Every piece of information a computer processes - from the text you read on screen to the videos you watch, from the games you play to the websites you visit - exists as a pattern of binary digits. But why do computers use binary, and how does a system with just two digits manage to represent the vast complexity of modern digital life?

Binary is a number system that uses only two digits: 0 and 1. Whilst humans typically use the decimal system (base-10) with ten digits (0-9), computers operate using the binary system (base-2). This fundamental difference between how humans and computers represent numbers stems from the physical nature of computer hardware itself.

The Physical Reality of Computer Circuits

Think of a simple light switch in your home. It has two reliable states: on and off. You would not design a light switch with ten different brightness levels because it would be difficult to distinguish between them reliably, and the switch mechanism would be far more complex and prone to errors. Similarly, electronic circuits are most reliable when they need to distinguish between just two states rather than multiple intermediate values.

When we represent data in binary, a 1 typically corresponds to "on" or a high voltage state (perhaps 5 volts), whilst a 0 corresponds to "off" or a low voltage state (perhaps 0 volts). This clear distinction between two states makes binary representation highly resistant to errors and interference, ensuring that data remains accurate as it moves through computer circuits.

Bits and Bytes: The Building Blocks of Digital Information

A single binary digit - either 0 or 1 - is called a bit, which is short for "binary digit". A bit is the smallest unit of data in computing. However, a single bit can only represent two possible values, which is not sufficient for most computing tasks. To represent more complex information, computers group bits together.

The most common grouping is eight bits, which forms a byte. A byte can represent 256 different values (from 00000000 to 11111111), calculated as 2⁸ = 256. This is sufficient to represent all the letters, numbers, and common symbols used in English text, which is why bytes became the standard unit for character encoding systems like ASCII.

Larger groupings of bits are used for different purposes: a nibble (4 bits) can represent 16 values, whilst a word (commonly 32 or 64 bits in modern computers) can represent enormous ranges of values. These different groupings allow computers to efficiently store and process everything from simple characters to very large numbers and complex data structures.

How Binary Represents Different Types of Data

Representing Numbers

Binary numbers work on the same principle as decimal numbers, but with powers of 2 instead of powers of 10. In the decimal number 2,547, each digit position represents an increasing power of 10 (ones, tens, hundreds, thousands). Similarly, in binary, each bit position represents an increasing power of 2.

For example, the binary number 1011 represents: (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = 8 + 0 + 2 + 1 = 11 in decimal. This place value system allows binary to represent any whole number, though it requires more digits than decimal to represent the same value.

Advantages of Binary for Computing

Reliability and Error Resistance

Binary's two-state system offers exceptional reliability. Electronic circuits can easily distinguish between a high voltage (representing 1) and a low voltage (representing 0), even when there is electrical noise or interference. If computers used a decimal system with ten voltage levels, it would be far more difficult to distinguish between adjacent levels reliably, leading to frequent errors.

This reliability becomes critical when considering that modern processors perform billions of operations per second, and data storage devices must maintain information accurately for years. The clear distinction between binary states ensures that data integrity is maintained through countless operations and transmissions.

Simplicity of Logic Circuits

Binary representation allows computers to use simple logic gates (AND, OR, NOT, XOR) to perform all computational operations. These logic gates are built from transistors and can be combined to create complex circuits that perform arithmetic, make decisions, and process data. The two-state nature of binary makes these circuits straightforward to design, manufacture, and operate reliably.

All arithmetic operations, from simple addition to complex mathematical functions, can be built from combinations of these basic binary operations. For example, adding two binary numbers follows simple rules: 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, and 1 + 1 = 10 (with a carry). These simple rules can be implemented in hardware using just a few transistors.

Deep Dive: Why Not Decimal or Other Number Systems?

Historically, there were attempts to build computers using decimal (base-10) representation, which would seem more natural since humans use decimal. The ENIAC, one of the first electronic computers built in the 1940s, actually used decimal representation. However, decimal computers faced significant challenges that ultimately led to binary becoming the universal standard.

Representing decimal digits electronically requires distinguishing between ten different voltage levels (0-9), which is far more complex and error-prone than distinguishing between just two levels. The circuitry needed to reliably detect and maintain ten distinct states is considerably more complicated than binary circuits. Additionally, decimal arithmetic circuits require more complex logic than binary arithmetic circuits.