00:02
Hello, to convert the base, to convert the base strain number 1 by 8 to binary, we can use the method of multiplying by 2 and taking the integer part of the result, we repeat the process until the fractional part become 0, until we obtain the desired number of binary digit.
00:30
We have 1 by 8, we will multiply 2, that is 0 .125, which is greater than 0.
00:37
So, we will take, which is less than 1, which is less than 1, so we will take 0.
00:48
Similarly, 0 .125 into 2 is equal to 0 .25, which is less than 1, so we are taking 0.
01:01
0 .25 into 2 is equal to 0 .5, that is less than 0, less than 1, we will take 1, we will take 0.
01:16
And 0 .5 into 2 is equal to 1, which is equal to 1, so we will take 1.
01:25
Therefore, the binary representation of 1 by 8 is 0 .001.
01:49
Now to express the floating point number using the rounding to nearest rule, we need to determine the exponent p and the mantissa m.
02:00
The mantissa m is obtained by normalizing the binary number and removing the leading zero.
02:06
So, we have 0 .001 equal to 1 .0 into 2 to the power minus 3...