Further Famous Bit Patterns

Say that a number is represented with all ones right to left and then all zeros, like this: 0111 1111. To find the decimal equivalent, turn on the next highest bit and turn off all others and subtract one, like this: 1000 0000 - 1. Now look up the decimal value corresponding to the single "on" bit: 1000 0000 - 1 = 128 -1 = 127.

Here is another table of bit patterns (regarded as representing positive integers) and their decimal equivalent. See if you can notice something interesting.

  Binary        Decimal       Notes
---------       -------      ------
0000 0001          1         
0000 0010          2          1 × 2
0000 0100          4          2 × 2
0000 1000          8          4 × 2

0000 0011          3
0000 0110          6          3 × 2
0000 1100         12          6 × 2
0001 1000         24         12 × 2

0000 0111          7 
0000 1110         14          7 × 2
0001 1100         28         14 × 2
0011 1000         56         28 × 2