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Half-adder and full-adder using logisim software

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The half-adder  A B S cin 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1  S is 1 when there is an odd number of 1s.=>A XOR B cin is 1 only when both inputs are 1.=>A AND B The full-adder A B Cin S C 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 Simplifying for S using K map and boolean algebra, we get (A XOR B) XOR Cin for S and Cin(A XOR B) OR AB
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Using NAND as universal gate

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Logisim is the software being used to draw the circuits and display the truth-tables. NAND gate Truth table of NAND gate Implementing NOT gate using NAND A NAND A = A' Truth table of A NAND A OR gate Truth table of OR gate Output is 1 when at least 1 input is 1. Implementing OR using NAND (A.B)' = A' +B' A OR B = A + B We just need to complement the inputs of A and B before feeding them to the NAND gate. Truth table  Truth table is same as that of OR gate AND gate A NAND B = (A.B)' A AND B = ((A.B)')' Just complement the output of NAND Truth table Output is 1 only when all inputs are same which is same as AND gate. Thank you for learning NAND gate as universal gate with me !
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