Binary Numbers
Binary is a number system that only uses the numerals 1 and 0. Our regular number system, Denary, uses 10 numerals : 0, 1 ,2 ,3 ,4 ,5 ,6 ,7 ,8 ,9.
Number systems use a concept called place value. You are already familiar with this concept even if you don't remember / recognise the word.
In Denary (our regular number system) the place values are as follows:
| Place value | 1,000 Thousands | 100 Hundreds | 10 Tens | 1 Ones / units |
| Numerals | 3 | 4 | 1 | 9 |
We know that this number means 3419, three thousand(s), four hundred(s) and nineteen.
We can break it down into: (3*1000) + (4*100) + (1*10) + (9*1)
Binary works the same way, just with different place values and only the numerals 1 and 0
This is equal to / the equivalent of the Denary number 11
| Place value | 8 (eights) | 4 (fours) | 2 (twos) | 1 (ones ) |
| Numerals | 1 | 0 | 1 | 1 |
We can break this down to see how it is equal to Denary 11: (1*8) + (0*4) + (1*2) + (1*1).
You might be thinking but why does it have those place values:
In Denary the place value is based on powers of 10. I use the ^ symbol to show powers so 10^2 is 10*10 (10 squared), and 10^3 is 10*10*10 (10 cubed)
- 10^0 = 1
- 10^1 = 10
- 10^2 = 100
- 10^3 = 1,000
Why 10? Because there are 10 numerals. Another way to refer to the Denary number system is Base 10.
In Binary, there are 2 numerals (0 and 1), so the place value is based on the powers of 2, and Binary is sometimes called base 2. If you are thinking why only 2 numerals, remember they represent On and Off.
- 2^0 = 1
- 2^1 = 2
- 2^2 = 4
- 2^3 = 8
- 2^4 = 16
- 2^5 = 32
- 2^6 = 64
- 2^7 = 128
I have gone to 2^7 (or 128) as binary is usually written with 8 numerals, not the 4 I used in the example above (I used 4 to simpify it and make it easier to follow)
It is worth knowing that sometimes people identify which Number System they are using for example:
I gave 10[Den] sweets to Claire and 10[Bin] sweets to Paul. Claire ended up with ten sweets, Paul ended up with two.