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author: Oldrich Pecak
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# Arithmetic circuits, multi-output circuits

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## Multi-output circuits

- basically multiple functions in one
- some optimalizations can be done
- most circuits are multi output

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## Half adder

- basic 1 bit adding
- two outputs
- can be built using 2 gates

|A|B|X|Carry|
|-|-|-|-----|
|0|0|0|0|
|0|1|1|0|
|1|0|1|0|
|1|1|0|1|

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## Full adder

- adds another input to half adder - carry in
- two outputs
- can be built using 5 gates or 2 half adders and a gate

|Cin|A|B|X|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|

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## Extending to multiple bits

- you can chain full adders - ripple carry adder
- first (LSB) adder can be half only
- one major problem with this approach