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ADDER, HALF ADDER & FULL ADDER

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Binary Addition 00 11 + 0 +1 01 1 10 Sum Carry Sum

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ADDER In electronics, an adder is a digital circuit that performs addition of numbers. In modern computers and other kinds of processors, adders are used in the arithmetic logic unit (ALU), but also in other parts of the processor, where they are used to calculate addresses, table indices, and similar operations. Although adders can be constructed for many numerical representations, such as binary-coded decimal or excess-3, the most common adders operate on binary numbers.

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Types of Adder There are two types of Adder 1.Half Adder 2.Full Adder

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Half Adder The half adder accepts two binary digits on its inputs A and B. It produce two binary digits outputs, a sum bit (S) and a carry bit (C). The simplest half-adder design, pictured incorporates an XOR gate for S and an AND gate for C. Carry<= X AND Y; Sum<= X XOR Y;

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Diagram A B (sum) C 0 (carry out) Half Adder Input Output Logic Symbol: Logic Diagram:

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Diagram Logic Diagram:

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Truth Table InputsOutputs XYCS 0000 0101 1001 1110

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Full Adder A full adder adds binary numbers and accounts for values carried in as well as out. A one-bit full adder adds three one-bit numbers input, often written as A, B, and C in ; A and B are the operands, and C in is a bit carried in. A full adder can be constructed from two half adders by connecting A and B to the input of one half adder, connecting the sum from that to an input to the second adder, connecting C in to the other input and OR the two carry outputs S = X xor Y xor Cin Cout = X.Y + X.Cin + Y.Cin

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Diagrams Logic Symbol: Logic Diagram: A B (sum) C 0 (carry out) Full Adder Input Output C in

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Diagram Half Adder Half Adder OR a b c in Sum C out

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Truth Table S is 1 if an odd number of inputs are 1. COUT is 1 if two or more of the inputs are 1. InputsOutput ABC in C out Sum 00000 00101 01001 01110 10001 10110 11010 11111

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Sum is `1’ when one of the following four cases is true: – a=1, b=0, c=0 – a=0, b=1, c=0 – a=0, b=0, c=1 – a=1, b=1, c=1

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A B Circuit of Adder

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A B X

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A B C in ∑ Circuit of Adder

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A B C in ∑ Y Circuit of Adder

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A B C in ∑ = A.B Y Circuit of Adder

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A B C in ∑ C out C out = (A B). C in + A.B Circuit of Adder

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The Full Adder X Y Cin S Cout

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The Full Adder Half Adder Cin Cin + xy

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