10001001 Introduction to Binary 10010001

Binary numbers --- Introduction --- Addition --- Multiplication --- Counter --- Card game

When we count using decimal or base 10, our normal counting system, we count up to nine using a different symbol each time: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Then for ten, we use two digits: 10. Beyond that, we combine the same ten symbols in various ways to give all possible numbers. This is called a positional system. So 3528 means three thousand, five hundred and twenty eight, or 3000 + 500 + 20 + 8. But you can count using less digits than this. You must have a zero. But you're not going to get anywhere with just zero! So you need a digit for one as well. This is called binary or base 2.

Enter a number in either box, and click on the button. Remember that binary numbers must only have ones and zeroes.

Number	Decimal	Binary	Comments
zero	0	0	Binary same as decimal
one	1	1	Binary same as decimal
two	2	10	Binary has run out of symbols, so needs two
three	3	11	10 (2) + 1
four	4	100	Binary run out of symbols again, three needed
five	5	101	100 (4) + 1 (no 10's)
six	6	110	100 (4) + 10 (2) (no 1's)
seven	7	111	100 (4) + 10 (2) + 1
eight	8	1000	Binary run out of symbols again, four needed

As you can see, binary numbers are usually longer than decimal numbers, and get even longer the bigger they get. You need twenty binary digits for a million. Also, the numbers are quite difficult to understand or remember, as they are strings of ones and zeros. This means that binary is not very useful for people. However, computers are good at remembering long numbers, and understand numbers whatever format they are in. Computers want numbers that they can hold easily in an electronic form, and where arithmetic is easy. In a computer, one means that an electrical current is flowing, and zero means that it is switched off. If you look at your TV, you may see that the on/off switch is marked 1 and 0. There are lots of ways that one is done in a computer - it gets tricky when you want to store numbers permanently, even when the computer is switched off. But this is essentially what all the numbers in a computer are.