Logical design of digital systems
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1 lectures Summer Semester 2017 Table of content 1 Combinational circuit design 2 Elementary combinatorial circuits for data transmission 3 Memory structures 4 Programmable logic devices 5 Algorithmic minimization approaches 51 Minimization of combinational Functions 52 State machine minimization 521 Characteristics of State Machines 522 Trivial state machine Simplification 523 Minimization according to Huffman & Mealy 524 The Moore Algorithm 6 Sequential circuit design 7 Testing digital circuits 2 1
2 State machine minimization 521 Characteristics of state machines Characteristics of state machines - Moore and Mealy Machines - 4 2
3 Characteristics of state machines - Synthesis of sequential circuits - Specify the problem, circuit behaviour Definition of In- and Output variables Derive state diagram/ state table/ type of state machine (Moore, Mealy, ) => Result: uncoded state table of a certain type of machine; eg Moore Machine State coding Calculate FF equations Design circuit for the output function Choose type of flip flop and calculate flip-flops flops input functions Design of the circuit for the state transition function Eventual transformation of the logical expressions into suitable structured expressions Application in the circuit diagram Characteristics of state machines - State machine tables - Transition Table Output Table x 1 x 2 x i x k x 1 X 2 x i x k z 1 n +1 z 2 z ij =g(x i,z j ) z j z l z 1 y ij=f(x i,z j ) z 2 z j z l 6 3
4 Characteristics of state machines - State machine tables - State transition table - of a Mealy-Machine - of a Moore Machine x 1 x 2 x i x k z 1 n+1 z 2 z ij / y ij z j z l z 1 x 1 x 2 x i x k zn+1 ij y 1 z 2 y 2 z j y u z l y v Characteristics of state machines - State transition diagramm - State tranistion table of JK-FF 1X Present State S1 S2 Input JK Out put 00 0I I0 II Q S1 S2 S2 S1 S2 S2 S1 S1 I 0 00 S1 0 X1 S J = don t care K=1 J = 0 K=0 Note, that an input that does not have any influence on a certain transition is marked with an X at the according arrow (don t care) 8 4
5 Characteristics of state machines - Timing diagrams - Z0 Z1 Z2 Z3 Z Trivial state machine minimization 10 5
6 Trivial state machine Simplification State machine minimization 523 Minimization according to Huffman & Mealy 12 6
7 State machine minimization 523 Minimization according to Huffman & Mealy Z n Z n+1 Y n Y n+1 X X State machine minimization 523 Minimization according to Huffman & Mealy 14 7
8 State machine minimization 524 Minimization according to Huffman & Mealy State machine minimization 523 Minimization according to Huffman & Mealy Z n Z n+1 Y n Y n+1 X X 0 0 I P I I I I I I I I I I I 0 Z n Z n+1 Y n Y n+1 X X 16 8
9 State machine minimization 523 Minimization according to Huffman & Mealy State machine minimization 523 Minimization according to Huffman & Mealy Z n Z n+1 Y n Y n+1 Z n Z n+1 Y n Y n+1 X X X X 18 9
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