21062017 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
21062017 52 State machine minimization 521 Characteristics of state machines 3 521 Characteristics of state machines - Moore and Mealy Machines - 4 2
21062017 521 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 5 521 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
21062017 521 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 7 521 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 S2 1 00 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
21062017 521 Characteristics of state machines - Timing diagrams - Z0 Z1 Z2 Z3 Z4 9 522 Trivial state machine minimization 10 5
21062017 522 Trivial state machine Simplification 11 52 State machine minimization 523 Minimization according to Huffman & Mealy 12 6
21062017 52 State machine minimization 523 Minimization according to Huffman & Mealy Z n Z n+1 Y n Y n+1 X X 0 1 2 3 4 5 6 7 13 52 State machine minimization 523 Minimization according to Huffman & Mealy 14 7
21062017 52 State machine minimization 524 Minimization according to Huffman & Mealy 15 52 State machine minimization 523 Minimization according to Huffman & Mealy Z n Z n+1 Y n Y n+1 X X 0 0 I 0 0 0 1 3 7 P I 0 2 6 0 I I 0 3 1 4 I I 0 4 5 0 0 I 0 5 2 0 I I 0 6 2 0 I I 0 7 5 0 0 I 0 Z n Z n+1 Y n Y n+1 X X 16 8
21062017 52 State machine minimization 523 Minimization according to Huffman & Mealy 17 52 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