Question

What is sum and carry?

Answer 1

In digital electronics and binary arithmetic, **sum** and **carry** refer to the basic operations of addition when working with binary numbers.

### 1. **Sum**:
The sum is the result of adding two binary digits (bits). For example:

- **0 + 0 = 0**
- **0 + 1 = 1**
- **1 + 0 = 1**
- **1 + 1 = 0** (but this is where the carry comes in, which I'll explain next)

The sum is the bit that is placed in the current column of a binary addition.

### 2. **Carry**:
The carry is the "extra" bit that is carried over to the next higher bit when the sum exceeds 1 in binary addition.

- **0 + 0 = 0** → No carry
- **0 + 1 = 1** → No carry
- **1 + 0 = 1** → No carry
- **1 + 1 = 10** → Sum = 0, carry = 1 (because 1 + 1 = 2 in decimal, which is 10 in binary)

In this case, the **carry** is the bit that moves to the next higher bit (like carrying over the 1 in decimal addition).

### Example of Binary Addition:

Let’s add two binary numbers:

```
  1 1 0 1  (13 in decimal)
+  1 0 1 1  (11 in decimal)
---------
  1 0 0 0 0  (24 in decimal)
```

**Step-by-step:**

1. Add the rightmost bits: 1 + 1 = 10. So, the sum is 0 and carry 1 to the next column.
2. Move to the next column: 0 + 1 + carry 1 = 10. The sum is 0, and carry 1 again.
3. Next column: 1 + 0 + carry 1 = 10. Sum is 0, carry 1.
4. Last column: 1 + 1 + carry 1 = 11. Sum is 1, and carry 1 is placed as the leftmost bit.

**Sum** is what we write down in the result, and **carry** is what gets moved to the next column during the addition.

In summary:
- **Sum** is the bit of the current column's result.
- **Carry** is the bit that gets passed to the next column if the sum exceeds 1 in binary.