Number Systems Explained: Binary, Decimal, and Their Role in Computer Hardware
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A computer is a device that performs a well-defined sequence of operations specified by a program. A computer combines two layers that depend on each other: hardware, the physical components you can touch, and software, the programs and instructions that tell the hardware what to do. Neither layer is useful without the other — hardware without software is inert, and software has nothing to run on without hardware.
How are the devices inside a PC connected?
All PC devices connect to the motherboard, which provides their interaction with the central processor, the RAM, the BIOS, and one another. The motherboard is the central hub through which every signal and data path travels, so it ultimately determines which components a computer can support.
PC devices divide into two groups: internal devices and external devices. Internal devices are installed inside the system unit alongside the motherboard, while external devices connect to ports and slots on the back of the PC case. Some devices can be either external or internal depending on their form — a modem or a magneto-optical disk drive, for example, exists in both versions.
How does a PC represent information?
A PC represents all information as numbers, and the processor works only with data encoded in numeric form. This single principle underlies every task a modern computer performs, from displaying text to playing video.
In the 1960s and 1970s, computers were called EDCMs — Electronic Digital Computing Machines — and were used mainly for mathematical calculations. Today the range of uses has expanded enormously: computers handle text processing, the creation of movies, communications, and even the writing of music. What has not changed is the underlying method of representing information — the processor still processes data encoded as numbers.
For a closer look at how a PC retains this numeric data, we recommend reading: Storing information in a PC.
What is a number system?
A number system is a way of writing numbers using a given set of special characters called digits. People are used to counting in tens — the decimal system — where each digit after 9 rolls over into a new position, so 10 means 1 ten plus 0 units. The position of a digit within a number is called the digit's place, or rank.
Places are counted from right to left, starting at zero. In the number 2978, for instance, the digit 8 sits in place zero and the digit 2 sits in place three. To find the value a numeral represents in any base, follow two steps:
- Multiply each digit in the record by the base of the number system (10 in the decimal case), raised to the power equal to that digit's place.
- Add the resulting values together.
Applying this to 2978 in the decimal system gives 2·10³ + 9·10² + 7·10¹ + 8·10⁰, which sums back to 2978. The same procedure works for any base — only the base value and the set of available digits change.
Why does a computer use the binary number system?
The central processing unit processes data represented in the binary number system because the hardware itself is built from two-state switches. At the heart of every microprocessor is the transistor key — a microelectronic device that can be in only one of two states, "closed" or "open."
These two states correspond to two levels of the source voltage: a high level, called the level of logical one, and a low level, the level of logical zero. Because each transistor naturally settles into one of just two voltage states, a number system with exactly two digits maps onto the hardware perfectly, with no ambiguity and maximum reliability.
Where each place in the decimal system can take ten values, from 0 to 9, each place in the binary system can take only two: 0 and 1. The decimal number 2 is written 10 in binary, meaning "1 two + 0 units." The decimal number 3 is written 11, meaning "1 two + 1 unit." Counting in binary follows the same roll-over rule as decimal counting — it simply rolls over after the digit 1 instead of after 9.
Written out in full, the decimal number 1998 becomes 11111001110 in binary, that is 1·2¹⁰ + 1·2⁹ + 1·2⁸ + 1·2⁷ + 1·2⁶ + 0·2⁵ + 0·2⁴ + 1·2³ + 1·2² + 1·2¹ + 0·2⁰. The binary form is longer to read, but for a machine built on two-state switches it is the most direct possible representation.
