Check a Half Adder's Two Outputs

Check both output places, then explain what the result can and cannot tell you.

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Inputs A and B are bits: each is 0 or 1. Sum = A XOR B is 1 when the inputs differ. Carry = A AND B is 1 only when both are 1. Read Carry first as the twos place and Sum second as the ones place. Check A + B = 2 x Carry + Sum. Inclusive OR cannot replace XOR: OR stays 1 for input 11, but Sum must be 0. This ideal model describes logical values, not physical wiring.

Worked example

For A = 0 and B = 0, XOR gives Sum 0 and AND gives Carry 0. Binary 00 represents zero. For A = 1 and B = 0, Carry/Sum is 01: 2 x 0 + 1 = 1. Reversing those inputs keeps the same total.

Inputs A and B both 1 enter XOR and AND. XOR gives Sum 0; AND gives Carry 1. The twos and ones output places read 10, meaning two. — Read both labeled output places. One Sum bit cannot store a total of two.

Would you believe it?

A binary adder can pass one column's carry-out to the next larger column's carry-in. The carried 1 has the next place's value, just as a carried digit changes place in ordinary column addition.

MIT OpenCourseWare: full adders and carry chains

Question 1 For A = 1 and B = 0, what are Carry and Sum, in that order? 1, 0 0, 0 0, 1

Question 2 A faulty adder uses OR for Sum. With input 11 it shows Sum 1. What should the correct Sum bit be? 0 1 2

Question 3 Carry is 1 and Sum is 0. What ordinary number does the output represent? 10 2 1

Question 4 Can adding just two input bits produce Carry 1 and Sum 1? Yes; input 11 produces output 11. Yes; either input can equal two. No; two input bits can total at most two.

Question 5 A half adder outputs Carry 0 and Sum 1. Which input pairs could have made it? 01 or 10 Only 11 Only 00

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