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Converting Numbers

Let's pull some results out of the table given earlier:

Decimal number	Same number in binary
1	1
2	10
4	100
8	1000

Each time the binary '1' moves one place to the left, it doubles in value in decimal. We can use this idea to convert from one system to the other.

Binary number					Decimal value
16	8	4	2	1
				1	1
			1	0	2
		1	0	0	4
	1	0	0	0	8
so
		1	1	1	7
	1	0	0	1	9
1	0	1	0	0	20
1	1	1	1	1	31

Did you spot the method?

In any binary number, the bit at the left-hand end has the highest value. This is known as the Most Significant Bit, (MSB). The one at the right-hand end is worth least, and is the Least Significant Bit, (LSB). For example:

MSB							LSB
1	0	0	1	0	1	1	1