Question

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

Answer 1

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.