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Aac boolean formulae

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marangburu42

The document discusses Boolean algebra formulae and techniques for converting gate circuits to Boolean expressions. It explains that gates can be converted to equivalent expressions using DeMorgan's Theorems. Sum-of-Products and Product-of-Sums Boolean expressions can be generated from truth tables and lend themselves to implementations using AND/OR gates.

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All-About-Circuits Boolean Algebra Formulae  To convert a gate circuit to a Booleanexpression, labeleachgate output with a Boolean sub-expressioncorresponding to the gates’ input signals, until a finalexpressionis reachedat the last gate. Exclusive OR  DeMorgan’s Theorems describe the equivalence betweengates with invertedinputs andgates with invertedoutputs. Simplyput, a NAND gate is equivalent to a Negative-ORgate, anda NOR gate is equivalent to a Negative-AND gate.  You must never attempt to breaktwo bars in one step!  Sum-Of-Products, or SOP, Boolean expressions maybe generated fromtruth tables quite easily, bydeterminingwhichrows of the table have an output of1, writingone product termfor eachrow, andfinallysumming all the product terms. Thiscreates a Boolean expressionrepresentingthe truth table as a whole.  Sum-Of-Products expressions lendthemselves wellto implementation as a set ofAND gates (products) feedinginto a single OR gate (sum).  Product-Of-Sums, or POS, Boolean expressions mayalsobe generatedfrom truthtablesquite easily, bydeterminingwhichrows of the table have an output of0, writingone sum termfor eachrow, andfinallymultiplyingallthe sum terms. Thiscreates a B oolean expression representingthe truth table as a whole.  Product-Of-Sums expressions lendthemselves wellto implementation as a set ofOR gates(sums) feeding intoa single AND gate (product).

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Aac boolean formulae

  • 1. All-About-Circuits Boolean Algebra Formulae  To convert a gate circuit to a Booleanexpression, labeleachgate output with a Boolean sub-expressioncorresponding to the gates’ input signals, until a finalexpressionis reachedat the last gate. Exclusive OR  DeMorgan’s Theorems describe the equivalence betweengates with invertedinputs andgates with invertedoutputs. Simplyput, a NAND gate is equivalent to a Negative-ORgate, anda NOR gate is equivalent to a Negative-AND gate.  You must never attempt to breaktwo bars in one step!  Sum-Of-Products, or SOP, Boolean expressions maybe generated fromtruth tables quite easily, bydeterminingwhichrows of the table have an output of1, writingone product termfor eachrow, andfinallysumming all the product terms. Thiscreates a Boolean expressionrepresentingthe truth table as a whole.  Sum-Of-Products expressions lendthemselves wellto implementation as a set ofAND gates (products) feedinginto a single OR gate (sum).  Product-Of-Sums, or POS, Boolean expressions mayalsobe generatedfrom truthtablesquite easily, bydeterminingwhichrows of the table have an output of0, writingone sum termfor eachrow, andfinallymultiplyingallthe sum terms. Thiscreates a B oolean expression representingthe truth table as a whole.  Product-Of-Sums expressions lendthemselves wellto implementation as a set ofOR gates(sums) feeding intoa single AND gate (product).