Binary Number 0 and 1

Used to describe a number system, or a number belonging to it, that has 2 rather than 10 as its base For instance, in a system called binary-coded decimal, each of the decimal digits 0 to 15 is coded in 4 bits.

Decimal
Base 10 2⁵ 2⁴ 2³ 2² 2¹ 2⁰
0 0 0 0 0
1 0 0 0 1
2 0 0 1 0
3 0 0 1 1
4 0 1 0 0
5 0 1 0 1
6 0 1 1 0
7 0 1 1 1
8 1 0 0 0
9 1 0 0 1
10 1 0 1 0
11 1 0 1 1
12 1 1 0 0
13 1 1 0 1
14 1 1 1 0
15 1 1 1 1

Binary to Base 10

Base 10	Base 2 (binary)	How to calculate	Base 10
0	0000	0x2³+0x2²+0x2¹+0x2⁰	0+0+0+0
1	0001	0x2³+0x2²+0x2¹+1x2⁰	0+0+0+1
2	0010	0x2³+0x2²+1x2¹+0x2⁰	0+0+2+0
......
15	1111	1x2³+1x2²+1x2¹+1x2⁰	8+4+2+1

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Decimal
Base 10	2⁵	2⁴	2³	2²	2¹	2⁰
0			0	0	0	0
1			0	0	0	1
2			0	0	1	0
3			0	0	1	1
4			0	1	0	0
5			0	1	0	1
6			0	1	1	0
7			0	1	1	1
8			1	0	0	0
9			1	0	0	1
10			1	0	1	0
11			1	0	1	1
12			1	1	0	0
13			1	1	0	1
14			1	1	1	0
15			1	1	1	1