(c) Convert $$ 110010_{2}+10100_{2} $$ in a binary number.

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To convert and add the binary numbers $$ 110010_2 $$ and $$ 10100_2 $$, follow these steps:

### Step 1: Align the Numbers
First, align the numbers by their least significant bits (rightmost bits):

```
  110010
+ 010100
```

### Step 2: Add Binary Numbers
Add the numbers column by column from right to left, keeping track of any carry-over:

| Position | 6 | 5 | 4 | 3 | 2 | 1 |
|----------|---|---|---|---|---|---|
| $$110010$$ | 1 | 1 | 0 | 0 | 1 | 0 |
| $$010100$$ | 0 | 1 | 0 | 1 | 0 | 0 |
| **Sum**      | 1 | 0 | 0 | 0 | 1 | 0 |

**Detailed Addition:**

1. **Position 1 (Rightmost):** $$0 + 0 = 0$$ (Carry: 0)
2. **Position 2:** $$1 + 0 = 1$$ (Carry: 0)
3. **Position 3:** $$0 + 1 = 1$$ (Carry: 0)
4. **Position 4:** $$0 + 0 = 0$$ (Carry: 0)
5. **Position 5:** $$1 + 1 = 0$$ with a carry-over of $$1$$
6. **Position 6 (Leftmost):** $$1 + 0 + 1$$ (including carry) $$= 0$$ with a carry-over of $$1$$

Since there's a carry-over after the leftmost position, prepend $$1$$ to the result:

```
1 0 0 0 1 1 0
```

### Step 3: Final Result
The sum of $$ 110010_2 $$ and $$ 10100_2 $$ is:

$$
1000110_2
$$

**Verification in Decimal:**

- $$ 110010_2 = 50_{10} $$
- $$ 10100_2 = 20_{10} $$
- Sum: $$ 50 + 20 = 70_{10} $$
- $$ 70_{10} = 1000110_2 $$

This confirms the correctness of the binary addition.

**Final Answer:**

$$
1000110_2
$$
The sum of $$ 110010_2 $$ and $$ 10100_2 $$ is $$ 1000110_2 $$.

(c) Convert \( 110010_{2}+10100_{2} \) in a binary number.

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