How do you evaluate binary decimals? Like 111.111 in the base 2...and you have to convert it to base 10?

Answer 1

In base b, a number in each position represents a power of b, with the "ones" digit being the zero power (which is always 1). Here is a long-winded example for (familiar) base 10:

345.21 = 300 + 40 + 5 + .2 + .01 = 3*100 + 4*10 + 5*1 + 2*.1 + 1*.01 = 3*10^2 + 4*10^1 + 5*10^0 + 2*10^(-1) + 1*10^(-2).

It works the same for any other base. Just replace the 10 with whatever base you wish. Here is one for base 2:

101.001 = 1*2^2 + 0*2^1 + 1*2^0 + 0*2^(-1) + 0^2^(-2) + 1*2^(-3) = 4 + 1 + 1/8 = 5.125.

Each digit represents a multiple of a power of 2.

Answer 2

Round it off to 6 then divide by 7, multiply by 3.1247 and add 42

Answer 3

148762