What is the difference between parallel addition and serial addition?

Answer 1

Serial addition adds one piece of the numbers at a time. It walks the bits and works on each bit at a time. It adds a column, carries if necessary, then adds the next column.

The parallel addition strategy adds the whole thing at once. All the bits are tentatively added at the same time using more complex circuitry. It is faster overall, despite the propagation delay that carrying causes. While being much faster, it requires much more hardware - more transistors - more space - more heat - more electricity.

Analogy: When humans add two 3 digit numbers (e.g. 123+654) we usually add the right most digits (3+4) first, then the middle digits, then the left digits. This is 3 steps and would be considered serial. Computers do the same thing but in binary. A serial adder might only add one bit at a time and take 32 steps to add two 32 bit numbers. Or it might add 4 bits at a time and take 8 steps. A parallel adder does it in one step.

A personal computer might use the parallel strategy, where a simple calculator with limited battery life would be more likely to use the serial strategy.

Answer 2

Well, in serial addition the data containing your "carry over" value must propagate through each addition sequence. This process makes the process much slower relative to parallel methods. This is how we do basic math: lining the row of numbers up, adding furthest digits on right and "carrying over" the one to the next digit pair. Had you not done the math right-to-left you would have an error based on the amount of carry overs you would have generated.