Jump to navigation Jump to search An adder is a digital circuit that performs addition of numbers. Although adders can be constructed for many number representations, such as binary-coded decimal or excess-3, ripple carry adder pdf most common adders operate on binary numbers. The half adder adds two single binary digits A and B. The carry signal represents an overflow into the next digit of a multi-digit addition.
The simplest half-adder design, pictured on the right, incorporates an XOR gate for S and an AND gate for C. With the addition of an OR gate to combine their carry outputs, two half adders can be combined to make a full adder. Half adder using NAND gates only. Logic diagram for a full adder. A full adder gives the number of 1s in the input in binary representation. A full adder adds binary numbers and accounts for values carried in as well as out. A and B are the operands, and Cin is a bit carried in from the previous less-significant stage.
A full adder can be implemented in many different ways such as with a custom transistor-level circuit or composed of other gates. In this implementation, the final OR gate before the carry-out output may be replaced by an XOR gate without altering the resulting logic. Using only two types of gates is convenient if the circuit is being implemented using simple IC chips which contain only one gate type per chip. It is possible to create a logical circuit using multiple full adders to add N-bit numbers. Each full adder inputs a Cin, which is the Cout of the previous adder.
The gate delay can easily be calculated by inspection of the full adder circuit. Each full adder requires three levels of logic. The carry-in must travel through n XOR-gates in adders and n carry-generator blocks to have an effect on the carry-out. A design with alternating carry polarities and optimized AND-OR-Invert gates can be about twice as fast. Some other multi-bit adder architectures break the adder into blocks.
It is possible to vary the length of these blocks based on the propagation delay of the circuits to optimize computation time. By combining multiple carry-lookahead adders, even larger adders can be created. This can be used at multiple levels to make even larger adders. For example, the following adder is a 64-bit adder that uses four 16-bit CLAs with two levels of LCUs. Other adder designs include the carry-select adder, conditional sum adder, carry-skip adder, and carry-complete adder. If an adding circuit is to compute the sum of three or more numbers, it can be advantageous to not propagate the carry result.
Instead, three-input adders are used, generating two results: a sum and a carry. The sum and the carry may be fed into two inputs of the subsequent 3-number adder without having to wait for propagation of a carry signal. 8 input values to 4 output values. The carry-out represents bit one of the result, while the sum represents bit zero. Likewise, a half adder can be used as a 2:2 lossy compressor, compressing four possible inputs into three possible outputs. Such compressors can be used to speed up the summation of three or more addends. If the addends are exactly three, the layout is known as the carry-save adder.
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