Learning Objectives

Why A Computer Uses Binary

A computer is an electronic system. At the physical level, its circuits can be designed to distinguish reliably between two stable states. These states may be described in many ways, such as high voltage and low voltage, on and off, magnetised in one direction and magnetised in the opposite direction, or light present and light absent. Computer science represents the two states using the symbols 1 and 0.

Binary is therefore not used because humans find it convenient. It is used because two-state electronic systems are simple to build, fast to switch and comparatively resistant to small variations in electrical signals. A value that is slightly above or below an expected voltage can still be interpreted as one of two states.

Every type of data must be converted to binary before the processor can work with it. Numbers, characters, images and sound are represented as patterns of bits. Program instructions are also represented in binary machine code. Logic gates process the bits, while registers and memory locations store them.

A binary pattern has no meaning by itself. Meaning comes from the rules used to interpret it. For example, the pattern 01000001 could be interpreted as the denary integer 65, the character A in an ASCII-based character set, or part of a pixel value. The program and data format determine which interpretation is correct.

• Input devices convert real-world or human-readable data into binary.
• The CPU processes binary instructions and binary data.
• Memory and secondary storage hold binary patterns.
• Output devices convert processed binary data into a form people or other systems can use.

Positional Number Systems

Denary, binary and hexadecimal are positional number systems. The value of a digit depends on both the digit itself and the column in which it appears. Moving one column to the left multiplies the place value by the base of the number system.

In denary, the base is 10, so place values are powers of 10: 1, 10, 100, 1000 and so on. In binary, the base is 2, so place values are powers of 2: 1, 2, 4, 8, 16 and so on. In hexadecimal, the base is 16, so place values are powers of 16: 1, 16, 256, 4096 and so on.

The rightmost position has exponent zero. This is why the rightmost place value is always 1: any non-zero base raised to the power 0 equals 1. For positive integers in this syllabus, positions to the left use increasing non-negative powers.

Understanding An 8-Bit Register

An 8-bit register has eight positions. When it stores a positive unsigned integer, the place values are 128, 64, 32, 16, 8, 4, 2 and 1. The smallest value is 00000000, which is 0. The largest is 11111111, which is 255 because all place values are added.

The leftmost bit is the most significant bit because changing it changes the value by 128. The rightmost bit is the least significant bit because changing it changes the value by only 1. These terms describe position and significance, not whether a bit is currently 0 or 1.

The maximum positive unsigned value that can be stored in n bits is 2^n – 1. There are 2^n possible bit patterns, but one pattern represents zero. Therefore, eight bits provide 256 patterns representing values 0 to 255.

Comparing The Three Number Systems

Meaning Of The Same Bit Pattern

Worked Examples

Examination Guidance

• Use the word binary when explaining how a computer represents all forms of data.
• Do not say that the computer understands letters or pictures directly. It processes binary codes that represent them.
• When asked why binary is used, connect the answer to two-state electronic circuits and reliable processing.
• Distinguish a bit pattern from its interpretation.

Knowledge Check

1. Why must text be converted to binary before it is processed?

2. How many different patterns can be represented using 10 bits?

3. What is the most significant bit?

4. State the base of hexadecimal.

5. Why can the same bit pattern have different meanings?