Boolean Algebra (Binary Logic)

[Pages:20]Boolean Algebra (Binary Logic)

Theorem

A + 0 = A A + 1 = 1 A+A=A A + A' = 1

A + B = B + A (A + B) + C = A + (B + C) AB + AC = A(B + C)

A * 0 = 0 A * 1 = A A*A=A A * A' = 0

A * B = B * A (A * B) * C = A * (B * C) (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

A + 0 = A A + 1 = 1 A + A = A A + A' = 1

A + B = B + A (A + B) + C = A + (B + C) AB + AC = A(B + C)

=>

A' B

Z

A * 0 = 0 A * 1 = A A * A = A A * A' = 0

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

A

B

B

AB + AC

AB + AC

A

A

C

C

Boolean Algebra (Binary Logic)

More Theorem (DeMorgan)

(A + B)' = A' * B'

(A * B)' = A' + B'

Why NAND and NOR gates?

A

A

B

B

AB + AC

AB + AC

A

A

C

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 B

A B

Z

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