Topic Content:
- Addition in Other Bases
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 + 14267
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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