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Boolean Algebra (Binary Logic)

Boolean Algebra ( binary logic ). Theorem A+0=A A*0=0. A+1=1 A*1=A. A+A=A A*A=A. A + A' = 1 A * A' = 0. A+B=B+A A*B=B*A. (A + B) + C = A + (B + C) (A * B) * C = A * (B * C). AB + AC = 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' A'. Z Z. B B. A. B. A+0=A A*0=0. A+1=1 A*1=A. A+A=A A*A=A. A + A' = 1 A * A' = 0. A+B=B+A A*B=B*A. (A + B) + C = A + (B + C) (A * B) * C = A * (B * C). AB + AC = 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 ).

ASCII Table (7-bit) (ASCII = American Standard Code for Information Interchange) Decimal Octal Hex Binary Value (Keyboard)----- ----- --- ----- -----Choi = $43 $68 ...

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Transcription of Boolean Algebra (Binary Logic)

1 Boolean Algebra ( binary logic ). Theorem A+0=A A*0=0. A+1=1 A*1=A. A+A=A A*A=A. A + A' = 1 A * A' = 0. A+B=B+A A*B=B*A. (A + B) + C = A + (B + C) (A * B) * C = A * (B * C). AB + AC = 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' A'. Z Z. B B. A. B. A+0=A A*0=0. A+1=1 A*1=A. A+A=A A*A=A. A + A' = 1 A * A' = 0. A+B=B+A A*B=B*A. (A + B) + C = A + (B + C) (A * B) * C = A * (B * C). AB + AC = 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 ).

2 More Theorem (DeMorgan). (A + B)' = A' * B' (A * B)' = A' + B'. Why NAND and NOR gates? 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. Z. B. Boolean Algebra ( binary logic ). More Function (Exclusive OR). Z = AB' + A'B Z=A B. A. A Z. B. 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 Interchange). Decimal Octal Hex binary Value (Keyboard). ------- ----- --- ------ ----- Choi = $43 $68 $6F $69.

3 ASCII Table (7-bit). (ASCII = American Standard Code for Information Interchange). Decimal Octal Hex binary Value (Keyboard). ------- ----- --- ------ ----- Choi = $43 $68 $6F $69. 0100 0011 => C'. C = $43. 0100 0011 => MSB odd parity ASCII Table (7-bit). (ASCII = American Standard Code for Information Interchange). Decimal Octal Hex binary Value (Keyboard). ------- ----- --- ------ ----- Choi = $43 $68 $6F $69. 0100 0011 => C'. C = $43. 0100 0011 => MSB odd parity 1100 0011 => MSB even parity ASCII Table (7-bit). (ASCII = American Standard Code for Information Interchange). Decimal Octal Hex binary Value (Keyboard). ------- ----- --- ------ ----- Choi = $43 $68 $6F $69. 0100 0011 => C'. C = $43 0110 1111 => o'. o = $6F. 0100 0011 => MSB odd parity 1110 1111 => MSB odd parity 1100 0011 => MSB even parity 0110 1111 => MSB even parity 100 0011 => C' = $43 110 1111 => o' = $6F.

4 0100 0011 => MSB odd parity 1110 1111 => MSB odd parity 1100 0011 => MSB even parity 0110 1111 => MSB even parity P it Circuit Parity Ci it D7 D6 D5 D4 D3 D2 D1 D0 = P. 0100 0011 => C' = $43. 0100 0011 => MSB odd parity 1100 0011 => MSB even parity D6 D5 D4 D3 D2 D1 D0 =P. 1 0 0 0 0 1 1 =P. Even Parity 1 1 0 0 0 0 1 1. D7 D6 D5 D4 D3 D2 D1 D0. Z=A B.


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