00:01
Hello students, this question is on number conversions.
00:05
In the question we are given a decimal number that is 65 ,535.
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And first we have to convert this into binary format.
00:16
For this, we'll make use of table of powers of 2.
00:21
Here we have table of powers of 2.
00:25
First of all, we have to look for power of 2, that is, lesser than or equal, to the given number.
00:34
The given number is 65 ,535.
00:39
So here power of 2 that is lesser than the given number it is 2 to the power 15.
00:46
So we have to subtract this power from the given number.
00:50
So minus 32 ,768.
00:54
This comes out to be equal to 32 ,76767.
01:00
Corresponding to the power, we would write 1 in the binary number.
01:05
So 2 to the power of 15 corresponding to it we would write 1 here.
01:10
Now again we have to look for a number that is smaller than or equal to the given number that is 32 ,767.
01:20
So first we'll write down here 32 ,767 and the power of 2 lesser than this number it is 2 to the power 14.
01:30
We'll subtract 16 ,384.
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This comes out to be equal to 16 ,383.
01:40
So here, corresponding to 2 to the power 14, we would write one here.
01:47
Again, we have to look for power of 2 lesser than or equal to this number, that is 2 to the power 13.
01:56
We'll subtract 16 ,383 minus 2 to 3 .3.
02:01
The power 13 that is 8192 this comes out to be equal to 8191 corresponding to 2 to the power 13 that is 8192 we would write 1 in the binary number again we will look for a number that is smaller than 8191 that is 4096 2 to the power 12 so we will write 8191 minus 4096 this comes out to be equal to 4095.
02:35
2 to the power 12 that is 4096 here corresponding to it we would write 1 here and this would go on.
02:46
We have to continue this process until we get 0 as different and corresponding to these powers of 2 we would write 1 in the binary number.
02:58
So here we would get this number...