Further Famous Bit Patterns

Say that a number is represented with all ones on the right and all zeros on the left, like this: 0011 1111. To find the decimal equivalent, turn on the bit to the left of the left-most one and then turn off all other bits. Compute the decimal equivalent of the resulting pattern and then subtract one.

For example, the equivalent of 0011 1111 is 0100 0000 - 1. The decimal value corresponding to the single "on" bit is 64 and 64 - 1 = 63.

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