00:01
So, in question a, we have to convert 10001 001 from binary to decimal.
00:10
So, from the right hand side, we will write 2 to the power 0, 2 to the power 1, 2 to the power 2, 2 to the power 3, 2 to the power 4, 2 to the power 5, 2 to the power 6 and 2 to the power 7.
00:22
Now, we will start from the right hand side and multiply 1 by 2 to the power 0.
00:28
And we will do the same with the second term and we will multiply 0 by 2 to the power 1 and we will keep on doing it like this.
00:42
So, 0 times 2 to the power 2 plus 1 times 2 to the power 3 plus 0 times 2 to the power 4 plus 0 times 2 to the power 5 plus 0 times 2 to the power 6 and lastly 1 times 2 to the power 7.
01:00
So, as you can see, the term 0 doesn't really matter that much.
01:04
The only thing that matters are 1s.
01:06
So, first of all, this will be 1 and now this will be 1 times 2 to the power 3 which is 8 and there is 0s and the last term will be 128.
01:19
Adding all three together, we get 137 which is the decimal form of this number.
01:26
Now in question b, we have 0001001.
01:33
Now doing the same thing, 2 to the power 0, 2 to the power 1, 2 to the power 3, 2 to the power 4, 2 to the power 5, 6, 7.
01:43
Now, we will start from here and we will multiply 1 by 2 to the power 0 and we can ignore the 0 terms.
01:53
So, we will multiply 1 by 2 to the power 3 and the rest are 0 terms...