Create a Full Adder
Expand standard addition by accepting carry-overs from previous computational columns.
Processing Carries
A Half Adder adds two numbers beautifully, but it functionally breaks if you try to chain them together because it absolutely ignores ‘Carry bits’ spilling over from the previous mathematical column!
A Full Adder effectively addresses this by accepting three distinct inputs: A, B, and Carry In.
Cascading Architecture
Instead of wiring everything randomly, think modularly! A Full Adder is effectively just two individual Half Adders smashed together, bridged safely by a single trailing OR Gate.
Notice how complex the wiring topology becomes as logic compounds. Toggle all three inputs in the embedded simulator below to definitively prove 1 + 1 + 1 = Sum 1, Carry 1.
| A | B | Carry In | Carry Out | Sum |
|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 |
| 0 | 0 | 1 | 0 | 1 |
| 0 | 1 | 0 | 0 | 1 |
| 0 | 1 | 1 | 1 | 0 |
| 1 | 0 | 0 | 0 | 1 |
| 1 | 0 | 1 | 1 | 0 |
| 1 | 1 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 |
By sequentially linking multiple Full Adders in a row (Outputting a Carry directly into the Input Carry of the next module), you definitively construct a Ripple Carry Processor allowing you to rapidly compute arbitrarily large math!