Boolean Algebra (Binary Logic)

Boolean Algebra (Binary Logic)

20 Pages · 2008 · 140 KB · English

Boolean Algebra (Binary Logic) Parity circuits: even/odd Z. ASCII Table (7-bit) (ASCII = American Standard Code for Information Interchange) Decimal Octal Hex

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Boolean Algebra (Binary Logic) Theorem A + 0 = A A + 1 = 1 AAA A * 0 = 0 A * 1 = A A*A A A + A = A A + A’ = 1 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 AB + AC = A(B + C) (A + B) (A + C) = A + BC Boolean Algebra (Binary Logic) A’B’ + A’B + AB = A’ + B = Z A’ B’ => Z A’ B Z A’ B A B A + 0 = A A * 0 = 0 A + 1 = 1 A + A = A A + A’ = 1A * 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 B A C AB + AC B A C C C Boolean Algebra (Binary Logic) More Theorem (DeMorgan) (A + B)’ = A’ * B’ (A * B)’ = A’ + B’ WhyNANDandNORgates? A B A B Why  NAND and NOR gates? AB + AC B A C AB + AC B A C 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’BZ = A B Z A B Boolean Algebra (Binary Logic) More Function (Exclusive‐OR) Z = AB’ + A’B Z = A B Z A B A Z B’ Z A’ B Boolean Algebra (Binary Logic) Parity circuits: even/odd Z ASCII Table (7-bit) (ASCII = American Standard Code for Information Interchange) Decimal Octal Hex Binary Value (Keyboard) ------- ----- --- ------ ----- ASCII Table (7-bit) (ASCII = American Standard Code for Information

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