If we built a five-bit adder, that final carry would be an input to the fifth full adder, and we'd get, which is 16 in base 10.Īs usual, here's the four-bit adder as a circuit diagram made out of our full adder components. The adder worked correctly here: it set the final carry variable to 1, but that value was discarded because our function didn't do anything with it. The problem with fixed-size adders like this one (and the ones in all of our computers) is that they stop being "adders" in the everyday sense when numbers get too large.įor example, if we try to add 15 + 1, which should give us 16, we get 0 instead. # Check: 7 + 8 = 15 (the largest 4-bit number) This is still the same process from primary school: add each column of digits, possibly carrying a 1 over to the next column. The full adders will cascade into each other: the carry output of each full adder feeds the carry input of the next. To add multi-bit numbers, we need one full adder per bit. We could use Python's native integers, but keeping the bits explicit makes it clear that there's no magic involved. First, a note about representation: we'll represent multi-bit numbers with arrays of 0s and 1s.
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