|
|
|
|
|
|
|
There are no 256s.
1 128 leaves 124
1 64 leaves 60
1 32 leaves 28
1 16 leaves 12
1 8 leaves 4
1 4 leaves 0
0
0
1 1 1 1 1 1 0 0 |
|
|
|
|
|
|
|
|
Thus, the answer in binary is 1111 1100. |
|
|
|
|
|
|
|
|
Now, it turns out that if you treat this binary number as two sets of 4 digits, you can do a magical transformation. |
|
|
|
|
|
|
|
|
The right set is 1100. In decimal that is 12, or in hexadecimal it is C. |
|
|
|
|
|
|
|
|
The left set is 1111, which in base 10 is 15, or in hexadecimal is F. |
|
|
|
|
|
|
|
|
Putting the two hexadecimal numbers together is FC, which is the real value of 1111 1100. This shortcut always works. You can take any binary number of any length, and reduce it to sets of 4, translate each set of four to hexadecimal, and put the hexadecimal numbers together to get the result in hexadecimal. Here's a much larger number: |
|
|
|
|
|
|
|
|
The columns are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, and 32768. |
|
|
|
|
|
|
|
|
1 * 1 = 1
1 * 2= 2
1 * 4 = 4
0 * 8 = 0 |
|
|
|
|
|