Solve the following operation with binary numbers. Check your answer by converting the binary numbers to base 10 numbers, doing the operation on the base 10 numbers, and converting the answer back to base 2.
1100102
+ 10102
To solve this operation, we can add the binary numbers just like we would add decimal numbers:
1100102
+ 10102
_____________
1111002
To check our answer, let's convert these binary numbers to base 10 numbers and do the operation:
1100102 = 50
10102 = 5
50 + 5 = 55
Now, let's convert 55 back to a binary number:
55 ÷ 2 = 27 remainder 1
27 ÷ 2 = 13 remainder 1
13 ÷ 2 = 6 remainder 1
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Reading the remainders from the bottom up, we get: 1101112
So the binary representation of the base 10 sum 55 is 110111.
To solve the operation with binary numbers, we can follow these steps:
Step 1: Align the numbers vertically.
110010
+ 1010
________
Step 2: Start from the rightmost digits and work towards the left, performing the addition.
110010
+ 1010
________
111100
Step 3: Check the answer by converting the binary numbers to base 10 and doing the operation.
To convert the binary numbers to base 10:
Binary number 1100102 is equal to 50 in base 10.
Binary number 10102 is equal to 10 in base 10.
Performing the addition operation in base 10:
50
+ 10
______
60
Step 4: Convert the base 10 answer back to base 2.
The base 10 number 60 is equal to the binary number 1111002.
Therefore, the result of the operation 1100102 + 10102 is 1111002.