Full adder, A = 1, B = 1, Cin = 1 — adders
core1 + 1 + 1 = 11
Answer
S = 1, Cout = 1
Why this example is worth doing
Three ones sum to three, which is binary 11: sum bit 1, carry 1. It is the row that shows the full adder is genuinely a three-input device rather than a half adder with an extra pin, and it is the row most often got wrong by hand. The page presents S = A ⊕ B ⊕ Cin and Cout as the majority function, both derived from the eight-row table rather than quoted.
Try your own input in the Half adder & full adder. Truth tables, K-maps and circuits for both adders, and the ripple-carry chain.
How the answer is reached
The probed row
A = 1, B = 1, Cin = 1
Output table
| A | B | Cin | S | Cout |
|---|---|---|---|---|
| 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 |