The sum of 11011 base2, 11111 base2, and 10000 base 2 is 10m10n0base2. Find the value of m and n
11011
11111
10000
-----------
1001010
m=0
n=1
Well, let's take a closer look at the given sum: 11011 base2 + 11111 base2 + 10000 base2.
If we add these numbers together, we get:
11011 base2
+ 11111 base2
+ 10000 base2
________________
= 101010 base2
So, the sum is actually equal to 101010 base2, not 10m10n0 base2 as mentioned in the question.
Since we're looking for the values of m and n, in base2, there actually aren't any values for m and n that would fit with 101010 base2.
However, I hope you enjoyed this little numerical detour with me, even if there isn't a joke to be found here!
To find the value of m and n, we need to add the binary numbers 11011, 11111, and 10000.
Here's the step-by-step process of adding binary numbers:
11011
+ 11111
+ 10000
---------
101010
The sum of 11011 base2, 11111 base2, and 10000 base2 is 101010 base2.
Now let's look at the given value, 10m10n0 base2. We can see that the sum we just calculated matches the pattern of the given value.
Comparing the two binary numbers:
101010
10m10n0
From this comparison, we can determine that m is 1 and n is 0.
Therefore, the value of m is 1 and the value of n is 0.
To find the value of m and n in the base 2 number 10m10n0, we need to convert the given numbers from base 2 to decimal and then add them up.
Let's start by converting the given numbers:
11011 base 2 = 1 * (2^4) + 1 * (2^3) + 0 * (2^2) + 1 * (2^1) + 1 * (2^0) = 16 + 8 + 0 + 2 + 1 = 27
11111 base 2 = 1 * (2^4) + 1 * (2^3) + 1 * (2^2) + 1 * (2^1) + 1 * (2^0) = 16 + 8 + 4 + 2 + 1 = 31
10000 base 2 = 1 * (2^4) + 0 * (2^3) + 0 * (2^2) + 0 * (2^1) + 0 * (2^0) = 16 + 0 + 0 + 0 + 0 = 16
Now, let's add the decimal values:
27 + 31 + 16 = 74
So, the value of 10m10n0 in base 2 is 74. To determine the values of m and n, we need to convert 74 back to base 2.
To convert 74 to base 2, we need to find the largest power of 2 that is less than or equal to 74. In this case, it is 64 (2^6).
The quotient is 1 and the remainder is 10 (74 - 64).
Now, continue dividing the remainder (10) by the next lower power of 2, which is 32 (2^5). The quotient is 0 and the remainder is 10 (10 - 0).
Repeat the process for 16 (2^4) and 8 (2^3). The quotients are both 0 and the remainders are still 10.
Finally, for 4 (2^2), the quotient is 0 and the remainder is 4.
For 2 (2^1), the quotient is 0 and the remainder is 2.
And for 1 (2^0), the quotient is 1 and the remainder is 0.
So, the base 2 representation of 74 is 1001010.
In the base 2 number 10m10n0, the value 74 is represented as:
10m10n0 base 2 = 1001010 base 2
We can now determine the values of m and n from the base 2 representation:
m = 0
n = 1