Hexadecimal Numbers

Introduction to Hexadecimal Numbers

Hexadecimal is a numbering system based on 16.
The system uses sixteen distinct symbols, digits 0-9 and letters A-F, represented as base-16.
A-F represent the decimal numbers 10 to 15 respectively.
Hexadecimal is commonly used in computing, for simplifying binary coding and for memory addressing.

Hexadecimal numbers are read from right to left and each digit represents a power of 16.
The right-most digit represents 16⁰, the next digit represents 16¹, then 16², and so on.
For example, the hexadecimal number 2B3 can be converted to a decimal number by calculating (3 * 16⁰) + (11 * 16¹) + (2 * 16²), giving the decimal equivalent as 691.

To convert from decimal to hexadecimal, divide the decimal number by 16 and take the remainder. The quotient is then divided by 16 again and this process is repeated until the quotient is zero. The hexadecimal equivalent is the series of remainders in reverse order.
To convert from hexadecimal to binary, each hexadecimal digit is replaced by its 4-digit binary equivalent.
Conversion from binary to hexadecimal is done by regrouping the binary number into sets of four, starting from the right, and replacing each group with its hexadecimal equivalent.

Hexadecimal is extensively used in computing and digital systems due to its ease and brevity in representing long strings of binary numbers.
It is used in memory addressing, where each byte in memory can be uniquely identified using hexadecimal.
Hexadecimal is widely used in programming, and it is important in understanding web colours, assembly language and machine code.

In web design, colours can be defined using hexadecimal values known as hex colour codes.
Each hex colour code contains 6 digits - the first two represent the red value, the middle two represent the green value, and the last two represent the blue value.
For example, the hex colour code for white is #FFFFFF, representing maximum values for red, green, and blue.

Exercising conversion between decimal, binary, and hexadecimal can build familiarity and fluency with hexadecimal numbers.
Creating hex colour codes can be a fun way to apply the concept in a practical context.