00:01
We now convert the base 2 number into base 10 equivalent.
00:05
So here we have the base 2 number that is 1 .10 .101.
00:11
And to convert this into base 10 number, we write the base 10 equivalent of each of the digits.
00:17
So first i write the base turn equivalent of this digit.
00:22
This digit is just before the decimal point.
00:25
So it's equivalent will be 2 raise to the power of 0.
00:28
And then we write the paste and equivalent of the next digit that is this will be two raised to the power of positive 1 now let's write the paste an equivalent of the digits after the decimal point so here this will be 2 raised to the power of 1 and for this digit this is 2 raise to the power of negative 1 and this is 2 raise to the power of negative 2 and for this digit this is 2 raised to the power of negative 3 and for the last digit this is 2 raised to the per of negative 1 and for the last digit this is 2 raise to the power of negative 1 and for the last digit this is 2 raised to the power of negative 4.
01:00
And now to write the base 10 equivalent, we basically multiply this digit with this value that is 1 times of 2 power 1.
01:12
And then we add the other digits.
01:14
This is 0 times of 2 power 0.
01:18
We then put plus and this will be 1 times of 2 power minus 1.
01:25
So likewise we do for the other that is this will be 0 times of 2 power negative 2 and then we have 0 times of 2 power negative 3 and finally we have the last digit that is 1 times of 2 power negative 4 and wherever we have the product of 0 we can simply cancel it this is a product of a number with the 0 and this one is also product of number with 0 and also this one so we have cancelled all the products with the has the number 0.
02:00
Now let's simplify this.
02:01
This is one times of 2 power 1 is 2.
02:04
So this one is 2.
02:06
This is 1 times of 2 power negative 1.
02:10
This is basically equivalent to 1 by 2 plus and this is 1 times of 2 power negative 4 which is 2 power negative 4 or 1 divided by 2 power 4.
02:25
And so this equals this equals 2 plus 1 by 2 is 0 .5 and this will be 1 divided by 2 power 4.
02:36
This basically equals 1 divided by 2 power 4 is 16 and 1 divided by 16 is 0 .0625...