Boolean Algebra (Binary Logic). Theorem. A + 0 = A. A + 1 = 1. A A A. A * 0 = 0 ...
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Boolean Algebra (Binary Logic) Theorem A+0=A A+1=1 A+A=A A + A’ = 1
A*0=0 A*1=A A*A=A A * A’ = 0
A+B=B+A (A + B) + C = A + (B + C) AB + AC = A(B + C)
A*B=B*A (A * B) * C = A * (B * C) (A + B)*(A B) (A + C) = A + BC
Boolean Algebra (Binary Logic) A’B’ + A’B + AB = A’ + B = Z A’ B’
=>
A’ B
Z
A’ B
Z
A B A+0=A A+1=1 A+A=A A + A’ = 1
A*0=0 A*1=A A*A=A A * A’ = 0
A+B=B+A (A + B) + C = A + (B + C) AB + AC = A(B + C)
A*B=B*A (A * B) * C = A * (B * C) (A + B)*(A + C) = A + BC
Boolean Algebra (Binary Logic) More Theorem (DeMorgan) (A + B)’ = A’ * B’
Boolean Algebra (Binary Logic) More Theorem (DeMorgan) (A + B)’ = A’ * B’
(A * B)’ = A’ + B’
Boolean Algebra (Binary Logic) More Theorem (DeMorgan) (A + B)’ = A’ * B’
(A * B)’ = A’ + B’
A B
A B AB + AC
A C
AB + AC A C
Boolean Algebra (Binary Logic) More Theorem (DeMorgan) (A + B)’ = A’ * B’
(A * B)’ = A’ + B’
Why NAND and NOR gates? Why NAND and NOR gates? A B
A B AB + AC
A C
AB + AC A C
Boolean Algebra (Binary Logic) More Function (Exclusive‐OR) Z = AB’ + A’B
Boolean Algebra (Binary Logic) More Function (Exclusive‐OR) Z = AB’ + A’B
Z=A A B
B
Z
Boolean Algebra (Binary Logic) More Function (Exclusive‐OR) Z = AB’ + A’B
Z=A A B
A B’ Z A’ B
B Z
Boolean Algebra (Binary Logic)
Parity circuits: even/odd Z
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Choi = $43 $68 $6F $69
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