#### 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.** 111100_{two} + 10111_{two} + 10011_{two}**2.** 110.011_{two} + 10.111_{two }+ 1.01_{two }**3.** 1304_{7} + 46_{7 }+ 1426_{7 }**4.** 5D6C_{16} + 6ABF_{16} + 3D2_{16}

**1.** 111100_{two} + 10111_{two} + 10011_{two}

**Solution**

**Explanation**

**1 ^{st} 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.

**2 ^{nd} 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.

**3 ^{rd }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.

**4 ^{th} 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.

**5 ^{th} 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.

**6 ^{th} 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 (7

^{th})column.

This yields 1100110_{two}

**2.** 110.011_{two} + 10.111_{two }+ 1.01_{two }

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