Electrical – binary addition / truth table

adderbinarytruth-table

I'm trying to understand how binary addition works.
If I understand it correctly, with two variables e.g. x and y you add a third one called c_i. On the other side, you add the sum and c_o.

The rules as far as I understood them: If you have two 1's, you carry 1 out and the result is 0.

Here is what confuses me:

1) In normal addition, you would carry in the 1 you carry out to the next line. Why don't we do this here, and therefore, what happens to the carry outs?

2) why is the carry in an "input" of its own, shouldn't it be just x and y since the carry ins/outs usually belong to one operation distinct from the values we use?

enter image description here

Thanks in advance!!

Best Answer

what happens to the carry outs?

You can combine n full adder circuits to make an adder for n-bit numbers. When you do this, you connect the carry-out from each adder to the carry ins of the adder for the next most significant bit.

Here's an example adding 2 3-bit numbers, X = A + B:

schematic

simulate this circuit – Schematic created using CircuitLab

why is the carry in an "input" of its own, shouldn't it be just x and y since the carry ins/outs usually belong to one operation distinct from the values we use?

It's more efficient to just calculate the sum of 3 bits in one operation than to add x and y, and then add cin in a 2nd step.

Related Topic