Expert: Pawan Musale - 3/27/2009

Question
how do you convert 1100101110 a binary number into a decimal nmumber?

Answer
Melissa,

While solving these types of problems, always mark POSITION for each digit. Position for Extreme right digit should be 0. The position for the next digit should be 1 and so on. So in this case, there are total 9 positions.


1     1    0    0     1     0    1    1    1     0 --> Digit
9     8    7     6     5    4    3    2    1     0 --> Positions

Now calculate 2 raise to (position number) i.e. for position 0, it is 2 raise to 0 which is 1. For position 1, it is 2 raise to 1 which is 2 and so on. So the calculation becomes

1     1    0    0     1     0    1    1    1     0 --> Digit
9     8    7     6     5    4    3    2    1     0 --> Positions
512  256  128   64     32   16   8    4    2     1 --> Calc

Now multiply (Digit * Calc). So it becomes:

1     1    0     0     1     0    1    1    1     0 --> Digit
9     8    7     6     5     4    3    2    1     0 -> Positions
512  256  128   64     32   16    8    4    2     1 -->Calc
512  256   0     0     32    0    8    4    2     0 --> Calc1

Now add all Calc1. i.e. 512 + 256 + 32 + 8 + 4 + 2 = 814

TIP - Observe above calculation carefully. At the last stage, we are multiplying 'Digit' with 'Calc'. So wherever Digit is 0, the result for that multiplication will be 0. So no need to find value of "Calc" for whom the Digit is 0. This will save the time.

I hope this will help you to understand the method to convert binary to decimal.

If the above calculations are not properly visible, let me know. I will send you bitmap of the same.

All the best.

Regards,
Pawan