Introduction to Computing?

[sameerrana]

Convert the following binary and decimal number into their respective number system.
i) 396 = ( ? )2

ii) 101011 = ( ? )10

 

[triden55]

To convert a binary number into decimal, you add the sum of the powers. We know that binary is base 2, therefore each digit represents a placeholder. For instance, in the number 0011, we can see that the least significant digit (the far right "1") is in the 2^0 spot. Anything to the power of zero is a "1" so the first digit is 1. The next digit over is 2^1, so this would be a "2". All the rest are zero so we won't worry about them. Now we add our results: 2+1 = 3 < answer.

Lets try another: 011011

Now break it up into powers of two starting with the right side.

This is what it will look like from right to left.

2^0 + 2^1 + 0 + 2^3 + 2^4 + 0 = 1 + 2 + 0 + 8 + 16 + 0 = 27

Use the same concept to convert your number.