Binary numbers --- Introduction --- Addition --- Multiplication --- Counter --- Card gameWhen 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.
|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|
© Jo Edkins 2006 - Return to Numbers index