Binary Number System
Computers use binary digits. And some puzzles can be solved using binary numbers.
A Binary Number is made up of only 0s and 1s.
110100 Example of a Binary Number
There is no 2,3,4,5,6,7,8 or 9 in Binary!
How do we Count using Binary?
| Binary | |
| 0 | We start at 0 |
| 1 | Then 1 |
| ??? | But then there is no symbol for 2... what do we do? |
Decimal
Well how do we count in Decimal?
| 0 | Start at 0 |
| ... | Count 1,2,3,4,5,6,7,8, and then... |
| 9 | This is the last digit in Decimal |
| 10 | So we start back at 0 again, but add 1 on the left |
The same thing is done in binary ...
|
Binary |
||
| 0 | Start at 0 | |
| • | 1 | Then 1 |
| •• | 10 | Now start back at 0 again, but add 1 on the left |
| ••• | 11 | 1 more |
| •••• | ??? | But NOW what ... ? |
Decimal What happens in Decimal ... ?
99 When we run out of digits, we ...
100 ... start back at 0 again, but add 1 on the left
And that is what we do in binary ...
Binary 0 Start at 0 • 1 Then 1 •• 10 Start back at 0 again, but add 1 on the left
|
Binary |
||
| 0 | Start at 0 | |
| • | 1 | Then 1 |
| •• | 10 | Now start back at 0 again, but add 1 on the left |
| ••• | 11 | |
| •••• | 100 | start back at 0 again, and add one to the number on the
left...
... but that number is already at 1 so it also goes back to 0 ... ... and 1 is added to the next position on the left |
| ••••• | 101 | |
| •••••• | 110 | |
| ••••••• | 111 | |
| •••••••• | 1000 | Start back at 0 again (for all 3 digits), add 1 on the left |
| ••••••••• | 1001 | And so on! |
Binary number is a number expressed in the binary numeral system or base-2 numeral system which represents numeric values using two different symbols: typically 0 (zero) and 1 (one). He base-2 system is a positional notation with a radix of 2.
|
Binary 8-bits word length: |
|||||||
| 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 |
| = 128 | = 64 | = 32 | = 16 | = 8 | = 4 | = 2 | = 1 |
Decimal vs Binary
Here are some equivalent values:
| Decimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| Binary 4-bits word length: |
0000 | 0001 | 0010 | 0011 | 0100 | 0101 | 0110 | 0111 | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 |
we start counting from the right
| 1 | 2 | 3 = 1 + 2 | 4 | 5 = 4 + 1 | 6 = 4 + 2 | 7 = 4 + 2 + 1 | 8 |
| 20 | 21 | 21 + 20 | 22 | 22 + 20 | 22 + 21 | 22 + 21 + 20 | 23 |
|
0001 |
0010 |
0011 |
0100 | 0101 | 0110 | 0111 | 1000 |
