Number Bases – A Level Computer Science AQA Revision

A number base, or radix, is the number of unique digits, including zero, used to represent numbers in a positional numeral system.
Base-10 is the decimal system we use in everyday life, composed of ten digits from 0-9.
Base-2 or binary, used extensively in computing, only uses two digits, 0 and 1.
Base-16 or hexadecimal, is also commonly used in computing. It uses sixteen distinct symbols, usually 0-9 to represent zero to nine, and A-F to represent values ten to fifteen.

Converting between number bases involves representing the same value in a different base.
Binary to decimal conversion involves summing up the products of each binary digit and 2 raised to the power of its position.
Decimal to binary conversion involves iteratively dividing by 2 and recording the remainders.
Conversion between binary and hexadecimal can be done easily as 16 is a power of 2 (2^4).

The binary system is fundamental to digital electronics and computing because it’s easy to represent binary digits, or bits, using two voltage levels.
Hexadecimal provides a more human-friendly way of representing binary sequences, as a single hexadecimal digit can represent a four-bit binary number (a nibble).
Understanding and being able to convert between number bases is critical when dealing with low-level programming, data manipulation, computer architecture, and networking, among other areas.