What is the decimal conversion of the binary number 1111 1111?

255. since number of 1's in "1111 1111" is 8 . we calculate decimal number as 2^8 = 256. starting from 0 to 255 .Hence the last(256th) number is 255.(sheetal)

General Purpose Answer

In decimal numbers, the digits have values that are powers of ten. Starting at the implied decimal point and working to the left, the number 403 is equal to:

3 x 100 + 0 x 101 + 4 x 102 = 3x1 + 0x10 + 4x100 = 3 + 0 + 400

In binary, the digits have values that are powers of two. Working to the left as before, the number 101 is equal to:

1 x 20 + 0 x 21 + 1 x 22 = 1x1 + 0x2+ 1x4 = (in decimal) 1 + 0 + 4 = 5

So, 1111 1111 = 1x1 + 1x2 + 1x4 + 1x8 + 1x16 + 1x32 + 1x64 + 1x128 = 255.

This also works to the right of the decimal point, but the powers of two are negative (i.e., fractions), so 101.011 in binary is:

1x1/8 + 1x1/4 + 0x1/2 + 1x1 + 0x2 + 1x4 = 5.375

Where the first digit to the right of the decimal point is 2-1 (one-half, or 1/2), the next is 2-2 (1/4), then 2-3 (1/8), etc.

Not sure I understand the logic behind the top answer. In this particular case, adding 1 to the original binary you get 1 0000 0000 which is 256, so take away the 1 again to get 255.