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In mathematics and mathematical logic, boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. Boolean algebra is used in the analysis and simplification of digital (logic) circuits
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Formulas for Carry out in a Full Adder
Boolean Algebra Approach
The equivalence of the two forms may be proven using boolean identities
Start off with the second expression
$$C_{out} = A B + (A \oplus B)C_{in}$$
Using the expansion,
$$ …