Lesson 1, Topic 4
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#### Topic Content:

When adding binary numbers some simple rules can be used.

The rules of binary addition are:

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 0 = 1
• 1 + 1 = 0 with a Carry of 1
• 1 + 1 + 1 = 1 with a Carry of 1

But we can also use another technique for the addition of binary and other bases, as shown below.

### Example 1.4.1:

Evaluate the following:

1. 111100two + 10111two + 10011two
2. 110.011two + 10.111two + 1.01two
3. 13047 + 467 + 1426
4. 5D6C16 + 6ABF16 + 3D216

1. 111100two + 10111two + 10011two

Solution

Explanation

1st Column (from right to left): 0 + 1 + 1 = 2. How many twos are there in 2? The answer is 1 remainder 0. Write 0 and carry 1 to column 2.

2nd Column: 1 + 0 + 1 + 1 = 3. How many twos are there in 3? The answer is 1 remainder 1. Write 1 and carry 1 to column 3.

3rd Column: 1 + 1 + 1 + 0 = 3. How many twos are there in 3? The answer is 1 remainder 1. Write 1 and carry 1 to column 4.

4th Column: 1 + 1 + 0 + 0 = 2. How many twos are there in 2? The answer is 1 remainder 0. Write 0 and carry 1 to column 5.

5th Column: 1 + 1 + 1 + 1 = 4. How many twos are there in 4? The answer is 2 remainder 0. Write 0 and carry 2 to column 6.

6th Column: 2 + 1 = 3. How many twos are there in 3? The answer is 1 remainder 1. Write 1 and carry 1 to the next (7th)column.

This yields 1100110two

2. 110.011two + 10.111two + 1.01two

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