Add Two Bits with Sum and Carry

Use a half adder and read its two outputs as binary places.

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A bit is 0 or 1. XOR gives 1 when two inputs differ. AND gives 1 only when both are 1. A half adder uses Sum = A XOR B and Carry = A AND B. Read Carry on the left (twos) and Sum on the right (ones). The total is 2 x Carry + Sum. These are logical values, not wiring instructions.

Worked example

For A = 1 and B = 1: Sum = 0 and Carry = 1. The result is binary 10, meaning 2 x 1 + 0 = 2, not ten.

With A and B both 1, XOR produces Sum 0 and AND produces Carry 1. Carry in the twos place and Sum in the ones place make binary 10, or two. — The Sum bit alone does not represent the whole total. Keep the Carry bit too.

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

Question 2 Which gate produces the Carry output of a half adder? XOR OR AND

Question 3 A two-bit binary number is 11. What ordinary number do those places represent? 11 2 3

Question 4 Which input pair makes a half adder produce Carry 0 and Sum 0? 00 01 11

Question 5 Why must we keep Carry as well as Sum? Carry always copies A. Sum alone confuses totals zero and two. Sum can hold the number two.

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