00:01
Hi there, in this problem we are going to deal with numbers in bases.
00:04
So we have to write a number which is written in base 10 and we have to convert it as a number in base other than 10.
00:12
We also have to find how can we write the sum of the numbers in bases other than 10.
00:19
How can we find the difference of the numbers in basis other than 10? and we have to describe the reason for the need of learning numbers with different bases.
00:28
So starting with the first thing that is how can we write a number in base 10 as a number in base other than 10? let us suppose a number in base 10 be given is 672 in base 10.
00:41
So this can be written as 6 multiplied by 10 raised to the power 2 plus 7 multiplied by 10 raised to the power 1 plus 2 multiplied by 10 based to the power 0.
00:54
So this is how we write it while expanding.
00:57
Now suppose we want to write it in base 10, okay? so in base 8.
01:05
So in base 8, first of all, we will see what is the highest power of 8 that does not exceed 670.
01:14
So we know that 8 raised to the power 1 gives 8.
01:20
8 raised to the power 2 will give 64 and 8 raised to the power 3 will give 512.
01:28
Further, 8 raised to the power 4 will give 4 ,096.
01:35
So we see that the 4th power exceeds 672.
01:41
Therefore we write the third power of 8 and we write 1 multiplied by 8 8 raised to the power 3.
01:49
Now we are going to subtract 672 minus 512 and this will give 0, 6, 6 and 1.
01:59
160.
02:02
Now we see that the third power will exceed 160 so we will use the second power of 8 and second power of 8 64 multiplied by 2 will give 128 so we can use 2 here extracting 160 minus 128 and it will give 32 the second power will exceed 32 so we will use the first power which is 8 x2 to the power 1 and 4 multiplied by 8 to the power 1 will give 32 so we can use 4 over here we are left with 0 therefore 0 multiplied by 8 raised to the power 0 now we're going to use these numbers and write the number in base 8 as 1 2 4 0 in base 8 so this is how we can write a number in base 10 as a number in the base other than 10.
03:06
Moving on to the second part, we have to find the sum of numbers in basis other than 10.
03:12
So suppose the numbers that are in basis other than 10 are given as 134 in base 8 and a number 256 in base 8...