Binary 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 both 𝑥 and 𝑦 are a sequence of digits each having a value of 0 or 1.
   • 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 binary point.
   • When expressed as decimal numbers, all binary digits are multiples of 2ⁿ, with n being the digit’s position relative to the binary point. Because of this, numbers expressed in the binary number system are said to be in base 2.
2. A radix of 2 can be appended to any number demonstrate it has been expressed in the binary number system, for example: 10110.011₂.
3. In the table below, each digit of the binary number 10110.011 is converted into a decimal number.
   • 1 x 2⁴ + 0 x 2³ + 1 x 2² + 1 x 2¹ + 0 x 2⁰ + 0 x 2^-1 + 1 x 2^-2 + 1 x 2^-3 = 22.375, which is 10110.011 expressed as a decimal number.

4. Position	4	3	2	1	0	.	-1	-2	-3
   Value of ‘1’	24	23	22	21	20	.	2-1	2-2	2-3
   Example binary number	1	0	1	1	0	.	0	1	1
   Decimal representation of digit	1 x 24	0 x 23	1 x 22	1 x 21	0 x 20	.	0 x 2-1	1 x 2-2	1 x 2-3