4.3 Combinational-Circuit Synthesis1.Approachto Circuit Designs> According to the descriptions of a circuit logicfunction, write the truth table≥ Transform the truth table into logic expression.> Simplify or transform the logic expression, andthen draw the logic circuit diagram.2.CircuitDescriptions> The description is a list of input combinationsExample:Given a 4-bit input combinationN=N,N2N,No, this function produces a 1 outputfor N=1,2,3,5,7,11,13, and 0 otherwise.ReturnNext
Example: Given a 4-bit input combination N=N3N2N1N0 , this function produces a 1 output for N=1,2,3,5,7,11,13, and 0 otherwise. ➢ According to the descriptions of a circuit logic function, write the truth table. 4.3 Combinational-Circuit Synthesis Return Next 1. Approach to Circuit Designs ➢ Transform the truth table into logic expression. ➢ Simplify or transform the logic expression, and then draw the logic circuit diagram. 2. Circuit Descriptions ➢ The description is a list of input combinations
4.3 Combinational-CircuitSynthesisF= Zng,Na,M.Mo(1,2,3,5,7,11,13) = N3 · N2 · N, · N。 +.N,.N. N, N.+N,·N2· N. No+N, N2·Ni.No+N, .N,.N,.No+N,·N2N.N.+N,:N,·N.N.The description is a word or sentence, callednatural’logic expression.Such a descriptionneed to be translated into algebraic expressions.Examples:(P215-217)BackNextReturn
4.3 Combinational-Circuit Synthesis Return Back Next Examples: (P215-217) ➢ The description is a word or sentence, called “natural” logic expression. Such a description need to be translated into algebraic expressions. 3 2 1 0 3 2 1 0 3 2 1 0 3 2 1 0 3 2 1 0 3 2 1 0 3 2 1 0 , , , 3 2 1 0 (1,2,3,5,7,11,13) N N N N N N N N N N N N N N N N N N N N N N N N F N N N N N N N N + + + + + = = +
4.3 Combinational-Circuit Synthesis3.Circuit ManipulationsNAND and NOR gates are faster than ANDsand ORs in most technologies. So, we needways to translate descriptions using AND, ORand NOT gates into other forms.An AND-OR circuit converts into aNAND-NANDs> We can obtain an equivalent sum-of-productsexpression for any logic expression. It may berealized directly with AND and OR gates. Theinverters required for complemented inputs arenot includedNextBackReturn
4.3 Combinational-Circuit Synthesis Return Back Next 3. Circuit Manipulations NAND and NOR gates are faster than ANDs and ORs in most technologies. So, we need ways to translate descriptions using AND, OR, and NOT gates into other forms. ➢ We can obtain an equivalent sum-of-products expression for any logic expression. It may be realized directly with AND and OR gates. The inverters required for complemented inputs are not included. ▪ An AND-OR circuit converts into a NAND-NANDs
4.3 Combinational-Circuit Synthesis> We may insert a pair ofinverters between AND-gate output and thecorresponding OR-gateinput in a two-level AND-OR circuit.8一8BackNextReturn
4.3 Combinational-Circuit Synthesis Return Back Next ➢ We may insert a pair of inverters between ANDgate output and the corresponding OR-gate input in a two-level ANDOR circuit
4.3 Combinational-CircuitSynthesis An OR-AND circuit converts into a NOR-NORs(See P219)4.Combinational-Circuit Minimization The methods to minimize a combinational circuitclassified two types:> Algebraic method> Karnaugh map methodMinimization usingthe algebraicmethodisdifficult to find terms that can be combined in ajumbleofalgebraicsymbolsNextBackReturn
4.3 Combinational-Circuit Synthesis Return Back Next (See P219) ▪ An OR-AND circuit converts into a NOR-NORs 4. Combinational-Circuit Minimization ▪ The methods to minimize a combinational circuit classified two types: ➢ Algebraic method. ➢ Karnaugh map method. Minimization using the algebraic method is difficult to find terms that can be combined in a jumble of algebraic symbols