Here is the solution to the seventh problem:
Now in order to convert any number from base 2 to base 10 U need to follow the following procedure wherein first of all U need to understand the following pattern:
......digit2 digit1 digit0 . digit(-1) digit(-2) digit(-3)........
U must carefully note that I have numbered the digits to the left of the decimal point as 0,1,2 and so on while on the right hand side of the decimal as -1,-2,-3 and so on.
Actually these digits represent powers of 2 with which we we will multiply them. It will be better to understand this with the solution of the above problem.
The answer has to consist of two parts: the one before the decimal and the one one after the decimal.
Let us first calculate the part before the decimal. The given number is 1101.011. The part before the decimal is 1101.
Now starting from the rightmost digit of 1101 multiply the digits of 1101 by increasing powers of 2 as 2^0, 2^1, 2^2and so on and add. So it becomes
(1 x 2^3) + (1 x 2^2) + (0 x 2^1) + (1 x 2^0)
= 8 + 4 +0 +1
= 13 which is the required answer before the decimal.
For the the part after the decimal U need to multiply by -ve powers of 2. So the part after the decimal is 011 which gives
(0 x 2^(-1) ) + (1 x 2^(-2) ) + (1 x 2^(-3) )
which is equivalent to
(0 x 1/2) + (1 x 1/4) + (1 x 1/
=0 + .25 + .125
=.375 which is the answer to the right of the decimal.
Combining the two results the final answer is 13.375 which is the required answer (not 13.357 what U've given here).
To simplify things just take a look below:
Digits: 1 1 0 1 . 0 1 1
Multipliers: 2^3 2^2 2^1 2^0 2^(-1) 2^(-2) 2^(-3)
i.e. 8 4 2 1 1/2 1/4 1/8
Increasing Decreasing
powers of <<---- ---->> powers of
2 2
Linear Mode
