Question

What is a carry-in?

Answer 1

A **carry-in** is a signal used in digital circuits, specifically in **binary addition**. It refers to the value carried over from a previous less significant bit during multi-bit addition.

Let me break it down for you:

When adding binary numbers, sometimes the sum of two bits results in a value greater than 1 (since in binary, 1+1 = 10). In this case, the **1** (which is the "carry") needs to be passed to the next more significant bit. For example:

- **1 + 1** gives a sum of **0** and a carry of **1** that moves to the next higher bit.

When you're working with a multi-bit adder, the **carry-in** is the carry from the previous bit. For example, if you're adding two 4-bit numbers, each bit addition will consider the carry-in from the previous less significant bit (starting with the carry-in for the least significant bit).

### Example:
Let’s say you are adding two binary numbers:

```
  1101
+ 1011
------
```

- Starting from the rightmost bit:
  - **1 + 1 = 10**. You write down **0**, and carry the **1** to the next column.
  - **0 + 1 + 1 (carry-in) = 10**. Write down **0**, carry the **1**.
  - **1 + 0 + 1 (carry-in) = 10**. Write down **0**, carry the **1**.
  - **1 + 1 + 1 (carry-in) = 11**. Write down **1**, carry the **1**.
  
So, the result looks like this:
```
   1101
+  1011
------
   11000
```

In this case, the carry-in for each addition after the first was the carry from the previous step.

In digital circuits like adders, the carry-in value is typically used as an input to each bit’s full adder, so that the correct result is obtained for multi-bit operations.