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Binary Numbering Link to heading

All computer data is represented using the binary number system.

Binary is base 2 and works with two digits, 0 and 1.

Binary numbers have some distinct advantages:

The simplicity of addition and subtraction
Binary information is easier to process due to having only two states (1 for ‘on’, 1 for ‘off’)
Less space consumed

Binary numbers are positional and each digit represents 2ⁿ, where n, starting from 0, is the position from the right.

Since there are 2 digits, each position represents a power of 2.

For example, to convert 11010011₂ to decimal.

11010011₁₀ = 1×2⁷ + 1×2⁶ + 1×2⁴ + 1×2¹ + 1×2⁰ = 128₁₀ + 64₁₀ + 16₁₀ + 2₁₀ + 1₁₀ = 211₁₀

Take each leftmost value, multiplied by 2 and added to the next value.

11010011₂

Position	Column Value	Decimal	Compared to Column Value	Resulting Action	Binary
8^th	128	211	Less than 256 but more than 128	Mark a 1 for the 8^th column and then subtract 128 from 215	1
7^th	64	87	More than 64	Mark a 1 for the 7^th column then subtract 64 from 87	1
6^th	0	23	Less than 32	Mark a 0 for the 6^th column	0
5^th	16	23	More than 16	Mark a 1 for the 5^th column and then subtract 16 from 23	1
4^th	0	7	Less than 8	Mark a 0 for the 4^th column	0
3^rd	0	7	More than 4	Mark a 1 for the 3^rd column and then subtract 4 from 7	1
2^nd	2	3	More than 2	Mark a 1 for the 2^nd column and then subtract 2 from 3	1
1^st	1	1	Equal to 1	Mark a 1 for the 1^st column	1

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