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Editing v0.34:Adder (Computing)
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==Look-ahead carry== | ==Look-ahead carry== | ||
− | While a simple adder is capable of reliable addition, it can be extremely slow. Consider a 8-bit adder: the value of the 8th bit depends on the carry derived from the 7th bit, which in | + | While a simple adder is capable of reliable addition, it can be extremely slow. Consider a 8-bit adder: the value of the 8th bit depends on the carry derived from the 7th bit, which in tun depends on the carry derived from the 6th bit, and so on. The entire addition has to be carried out sequentially, rather than adding the bits in parallel. Because of the way the carry ripples through the value, such systems are called ''ripple carry adders.'' When water or creatures are used in the circuits, this can mean a day or more to add two 8 bit values. However, the process can be improved considerably, at the expense of greater complexity, by implementing a look-ahead system. |
Look ahead systems break the values up into sequences of bits, based on the fact that if both values of the nth bit are 0 ((NOT[n])AND(NOT[n'])), any carry will end at that bit, and that if both values are 1 ([n]AND[n']), that bit will generate a carry. Based on this, it's possible to process, in parallel, the addition of various bit-lengths based on the knowledge that carries will not propagate past a carry-ending bit. This can vastly improve the time necessary to add two values. | Look ahead systems break the values up into sequences of bits, based on the fact that if both values of the nth bit are 0 ((NOT[n])AND(NOT[n'])), any carry will end at that bit, and that if both values are 1 ([n]AND[n']), that bit will generate a carry. Based on this, it's possible to process, in parallel, the addition of various bit-lengths based on the knowledge that carries will not propagate past a carry-ending bit. This can vastly improve the time necessary to add two values. |