The sum of three numbers in base two is 11101. If the first two numbers are 1011 and 1101 find the
third number?
Just add and subtract in base 2
x + 1011 + 1101 = 11101
x + 11000 = 11101
= 101
or , copping out and changing to base 10
10112 = 1110
11012 = 1310
111012 = 2910
y + 11 + 13 = 29
y = 5
and 510 = 1012 , as above
To find the third number, you can subtract the sum of the first two numbers from the given sum.
Given:
First number = 1011 (in base two)
Second number = 1101 (in base two)
Sum of three numbers = 11101 (in base two)
To subtract the sum of the first two numbers from the given sum, perform the following steps:
Step 1: Convert the first and the second numbers to base ten:
1011 (in base two) = 11 (in base ten)
1101 (in base two) = 13 (in base ten)
Step 2: Subtract the sum of the first two numbers from the given sum:
11101 (in base two) - (11 + 13) (in base ten) = 11101 (in base two) - 24 (in base ten)
Step 3: Convert the result back to base two to find the third number:
11101 (in base two) - 24 (in base ten) = 11001 (in base two)
Therefore, the third number is 11001 (in base two).
To find the third number, we need to subtract the sum of the first two numbers from the given sum.
First, let's convert the first two numbers to decimal form:
1011 in base 2 = (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = 8 + 0 + 2 + 1 = 11
1101 in base 2 = (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0) = 8 + 4 + 0 + 1 = 13
Now, let's add the decimal forms of the first two numbers:
11 + 13 = 24
Next, let's convert the given sum to decimal form:
11101 in base 2 = (1 * 2^4) + (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0) = 16 + 8 + 4 + 0 + 1 = 29
Finally, subtract the sum of the first two numbers from the given sum:
29 - 24 = 5
Therefore, the third number in base two is 101.