Boolean Algebra (Binary Logic)TheoremA + 0 = AA + 1 = 1AAAA * 0 = 0A * 1 = AA*A AA + A = AA + A’ = 1A * A = AA * A’ = 0A + 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 + BCAB + AC = A(B + C)(A + B) (A + C) = A + BCBoolean Algebra (Binary Logic)A’B’ + A’B + AB = A’ + B = ZA’B’=>ZA’BZA’BABA + 0 = A A * 0 = 0A + 1 = 1A + A = AA + A’ = 1A * 1 = AA * A = AA * A’ = 0A + 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 + BCBoolean 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’ABABAB + ACBACAB + ACBACCCBoolean Algebra (Binary Logic)More Theorem (DeMorgan)(A + B)’ = A’ * B’ (A * B)’ = A’ + B’Why NAND and NOR gates?ABABWhy NAND and NOR gates?AB + ACBACAB + ACBACCCBoolean Algebra (Binary Logic)More Function (Exclusive‐OR)Z = AB’ + A’BBoolean Algebra (Binary Logic)More Function (Exclusive‐OR)Z = AB’ + A’BZ = A BZABBoolean Algebra (Binary Logic)More Function (Exclusive‐OR)Z = AB’ + A’B Z = A BZABAZB’ZA’BBoolean Algebra (Binary Logic)Parity circuits: even/oddZASCII 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 $69ASCII Table (7-bit)(ASCII = American Standard Code for Information Interchange)Decimal Octal Hex Binary Value (Keyboard)------- ----- --- ------ -----Choi = $43 $68 $6F $690100 0011 =>‘C’= $430100 0011 => C = $430100 0011 => MSB odd parityASCII Table (7-bit)(ASCII = American Standard Code for Information Interchange)Decimal Octal Hex Binary Value (Keyboard)------- ----- --- ------ -----Choi = $43 $68 $6F $690100 0011 =>‘C’= $430100 0011 => C = $430100 0011 => MSB odd parity1100 0011 => MSB even parityASCII Table (7-bit)(ASCII = American Standard Code for Information Interchange)Decimal Octal Hex Binary Value (Keyboard)------- ----- --- ------ -----Choi = $43 $68 $6F $690100 0011 =>‘C’= $430110 1111 =>‘o’= $6F0100 0011 => C = $430100 0011 => MSB odd parity1100 0011 => MSB even parity0110 1111 => o = $6F1110 1111 => MSB odd parity0110 1111 => MSB even parity100 0011 => ‘C’ = $430100 0011 => MSB odd parity110 1111 => ‘o’ = $6F1110 1111 => MSB odd parity1100 0011 => MSB even parity 0110 1111 => MSB even parityPitCi itParity CircuitD7 D6 D5 D4 D3 D2 D1 D0 = P0100 0011 => ‘C’ = $430100 0011 => MSB odd parity1100 0011 => MSB even parityD6 D5 D4 D3 D2 D1 D0 = P1 0 0 0 0 1 1 = PEven Parity11 00 0 01 1Even ParityD7 D6 D5 D4 D3 D2 D1 D01 1 0 0 0 0 1 1Z = A
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