Carry look-ahead adder

A carry-lookahead adder (CLA) or fast adder is a type of adder used in digital logic. A carry-lookahead adder improves speed by reducing the amount of time required to determine carry bits. It can be contrasted with the simpler, but usually slower, ripple carry adder for which the carry bit is calculated alongside the sum bit, and each bit must wait until the previous carry has been calculated to begin calculating its own result and carry bits (see adder for detail on ripple carry adders). The carry-lookahead adder calculates one or more carry bits before the sum, which reduces the wait time to calculate the result of the larger value bits. The Kogge-Stone adder and Brent-Kung adder are examples of this type of adder.

Charles Babbage recognized the performance penalty imposed by ripple carry and developed mechanisms for anticipating carriage in his computing engines. Gerald Rosenberger of IBM filed for a patent on a modern binary carry-lookahead adder in 1957.

A ripple-carry adder works in the same way as pencil-and-paper methods of addition. Starting at the rightmost (least significant) digit position, the two corresponding digits are added and a result obtained. It is also possible that there may be a carry out of this digit position (for example, in pencil-and-paper methods, "9+5=4, carry 1"). Accordingly, all digit positions other than the rightmost need to take into account the possibility of having to add an extra 1, from a carry that has come in from the next position to the right.

This means that no digit position can have an absolutely final value until it has been established whether or not a carry is coming in from the right. Moreover, if the sum without a carry is 9 (in pencil-and-paper methods) or 1 (in binary arithmetic), it is not even possible to tell whether or not a given digit position is going to pass on a carry to the position on its left. At worst, when a whole sequence of sums comes to ...99999999... (in decimal) or ...11111111... (in binary), nothing can be deduced at all until the value of the carry coming in from the right is known, and that carry is then propagated to the left, one step at a time, as each digit position evaluated "9+1=0, carry 1" or "1+1=0, carry 1". It is the "rippling" of the carry from right to left that gives a ripple-carry adder its name, and its slowness. When adding 32-bit integers, for instance, allowance has to be made for the possibility that a carry could have to ripple through every one of the 32 one-bit adders.

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