## Full Adder and Subtractor SOLVED

 W, X, Y, Z are one bit numbers, using full/half adder and subtractor design the following operation : W+X-Y-Z. I seriously do not know what should i do to solve this and i couldn't understand it. Anyone can help please? by MarinaGoal May 13, 2020

### Answer by blasphemydog

 parenthesis () represent compliments. A half adder is used to add together two bits. The output will be two bits, a carry and the sum. Using a truth table and Kanaugh maps, the sum of a half adder is the two bits exclusive OR (XOR) together. The borrow is the two bits AND together. Use a half adder to add W and X. The outputs will be: sum = W(X) + (W)X which is W XOR X (exclusive OR), carry = WX As you can see, our output is two bits (sum, carry). Remember that a full adder/subractor is used for three bits. We have found the ouputs (2 bits) for W + X, and now must use a full subtractor in order to subtract Y from the previous result (a 3 bit operation). Using truth tables and Kanaugh maps, if the inputs to a full subtractor are A,B,C, then the outputs will be as follows: diff = A XOR B XOR C, borrow = (A)B + BC + (A)C Using our result for W + X above, Let A = sum Let B = carry Let C = Y Then the outputs from the full subtractor will be: diff = sum XOR carry XOR Y borrow = (sum)carry + carry.Y + (sum)Y Now, use a full subtractor again in order to subtract Z. Inputs are: diff, borrow, Z Outputs are: answer = diff XOR borrow XOR Z final borrow = (diff)borrow + borrow.Z + (diff)Z Review: half adder: inputs A,B then sum = A XOR B, carry = AB full subractor: inputs A,B,C then diff = A XOR B XOR C, borrow = (A)B + BC + (A)C Use a half adder on W,X. Output will be sum and carry. Use a full subtractor on sum,carry,Y. The outputs will be diff and borrow. Use a full subtractor on diff, borrow, Z. The final output will be answer and final borrow. Hope that helps. ACCEPTED +1 vote by blasphemydog May 14, 2020

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