Hexadecimal number system

1. A system which permits numbers to be expressed according to the following rules:
   • Numbers consist of two parts, 𝑥 and 𝑦 in the form 𝑥.𝑦, where 𝑥 and 𝑦 are a sequence of digits each having a one of sixteen values: 0-9, or A-F.
   • 0-9 have the same meaning as they do in the decimal number system.
   • A-F represent the decimal numbers 10 (A), 11 (B), 12 (C), 13 (D), 14 (E), 15 (F).
   • 𝑥 and 𝑦 are binary representations of the decimal numbers d & e respectively, such that |d| ≥ 1 and 0 ≤ |e| < 1.
   • The symbol separating 𝑥 from 𝑦 is called the hexadecimal point.
   • When expressed as decimal numbers, all hexadecimal digits are multiples of 16ⁿ, with n being the digit’s position relative to the hexadecimal point. Because of this, numbers expressed in the hexadecimal number system are said to be in base 16.
2. A radix of 16 can be appended to any number to remove any doubt it has been expressed in the binary number system, for example: 4F₁₆.
3. In the table below, each digit of the hexadecimal number 9AF17.BC1 is converted into the value it represents.
   • 9 x 16⁴ + 10 x 16³ + 15 x 16² + 1 x 16¹ + 7 x 16⁰ + 11 x 16^-1 + 12 x 16^-2 + 1 x 16^-3 = 634647.734619140625.

4. Position	4	3	2	1	0	.	-1	-2	-3
   Value of ‘1’	164	163	162	161	160	.	16-1	16-2	16-3
   Example hexadecimal number	9	A	F	1	7	.	B	C	1
   Decimal representation of digit	9 x 164	10 x 163	15 x 162	1 x 161	7 x 160	.	11 x 16-1	12 x 16-2	1 x 16-3