Question

Find the addition of the following numbers in binary: (124)7 and (456)7. Show all required steps to justify your answer, as per the addition algorithm for binary numbers.

Answer 1

The sum of 124 (7) and 456 (7) is 1001000100 (2).

Step-by-step explanation:

To add binary numbers, we follow a similar process as adding decimal numbers. However, we need to keep in mind that binary numbers only have two digits (0 and 1). Here is the step-by-step solution:

Step 1: Align the numbers vertically, with the rightmost digits aligned.

124

+ 456

-----

Step 2: Start from the rightmost column and add the digits. If the sum is 0, write 0. If the sum is 1, write 1.

124

+ 456

-----

1000

Step 3: If the sum of the current column and the carry from the previous column is 2, write 0 and carry 1. If the sum is 3, write 1 and carry 1.

124

+ 456

-----

10

01

Step 4: Repeat steps 2 and 3 until you reach the leftmost column.

124

+ 456

-----

1001000100

Therefore, the sum of 124 (7) and 456 (7) is 1001000100 (2).