Binary to decimal

Decimal numbers are to base 10. Let us count to 10. 1, 2, 3..... up to 9 and there is no single digit for 10 and that's why we say decimal system is base 10.

Binary numbers are to base 2. Let us count to 2. 1,... up to 1 (and that's it) and there is no single digit for 2 and hence binary system is base 2. In fact decimal-2 is binary-10 (this is read 'binary one zero' and not 'ten'), that is there is two digits for decimal-2 in binary form.

Conversion is easy. Let's look through an example and you should figure it out.

Let us convert binary-10001011 to decimal.

Binary

1 0 0 0 1 0 1 1

Decimal

Food for thought

· It seems if all digits of an 8-bit binary are zero then we get decimal 0 for it. What is the equivalent decimal for an -bit binary if all digits are 1? The answer is 255. Can you work it out? How many binary bits do we need to present decimal 256?

· How would you convert 139 back to its binary form?

· Do we have other numbering systems, say for example to base 8?

· If we do have to base 8, what would it be called?

· If we do have to base 8, how would it work?