Full Adder

ucla | CS M51A | 2023-01-10T14:35

Definitions

prime
- when the incoming bit is 0, denote its variable with a prime
- e.g. Xi’ denotes 0 bit while Xi denotes 1 bit

$Z i = X_{i}^{'} Y_{i}^{'} C_{i n} + X_{i}^{'} Y_{i} C_{i n}^{'} + X_{i} Y_{i}^{'} C_{i n}^{'} + X_{i} Y_{i} C_{i n}$

$Z_{i} = (X_{i} + Y_{i} + C_{i n}) (X_{i} + Y_{i}^{'} + C_{i n}^{'}) (X_{i}^{'} + Y_{i} + C_{i n}^{'}) (X_{i}^{'} + Y_{i}^{'} + C_{i n})$

singular addition unit with a carry forward capability and 2 parameters
can be placed in series to carry forward addition parameters and carry bits
truth table
equations can be written as:
- $Z i = (X i + Y i + C i) \dots (X i^{'} + Y i^{'} + C i^{'})$

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**SUMMARY
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