CS 140 Lecture 19 Standard Modules

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CS 140 Lecture 19 Standard Modules Professor CK Cheng CSE Dept. UC San Diego

Standard Sequential Modules Register Shift Register Counter

Counter Applications?

Counter: Applications Program Counter Address Keeper: FIFO, LIFO Clock Divider Sequential Machine

Counter Modulo-n Counter Modulo Counter (m<n) Counter (a-to-b) Counter of an Arbitrary Sequence Cascade Counter

Modulo-n Counter D CNT TC LD Clk CLR Q Q (t+1) = (0, 0, .. , 0) if CLR = 1 = D if LD = 1 and CLR = 0 = (Q(t)+1)mod n if LD = 0, CNT = 1 and CLR = 0 = Q (t) if LD = 0, CNT = 0 and CLR = 0 TC = 1 if Q (t) = n-1 and CNT = 1 = 0 otherwise

Modulo-m Counter (m< n) Given a mod 16 counter, construct a mod-m counter (0 < m < 16) with AND, OR, NOT gates Q3 Q2 Q1 Q0 3 2 1 0 CLK CLR CNT D3 D2 D1 D0 0 0 0 0 LD Q2 Q0 X m = 6 Set LD = 1 when X = 1 and (Q3Q2Q1Q0) = (0101), ie m-1

Counter (a-to-b) Given a mod 16 counter, construct an a-to-b counter (0 < a < b < 15) A 5-to-11 Counter Q3 Q2 Q1 Q0 CLR Clk CNT X D3 D2 D1 D0 LD Q3 (b) Q1 0 1 0 1 (a) Q0 Set LD = 1 when X = 1 and (Q3Q2Q1Q0) = b (in this case, 1011)

Counter of an Arbitrary Sequence Given a mod 16 counter, construct a counter with sequence 0 1 5 6 2 3 7 When Q = 1, load D = 5 When Q = 6, load D = 2 When Q = 3, load D = 7 Q2 Q1 Q0 Clk CLR CNT D2 D1 D0 LD Q2’ Q0 X Q2 Q0 Q1 Q0 Q0’

Counter of an Arbitrary Sequence Given a mod 16 counter, construct a counter with sequence 0 1 5 6 2 3 7 K Mapping LD and D, we get Id Q2Q1Q0 LD D2 D1 D0 000 - 1 001 2 010 3 011 4 100 5 101 6 110 7 LD = Q2’ Q0 + Q2Q0’ D2 = Q0 D1 = Q1 D0 = Q0

Counter of an Arbitrary Sequence Count in sequence 0 2 3 4 5 7 6 Id Q2Q1Q0 LD D2 D1 D0 000 1 001 - 2 010 3 011 4 100 5 101 6 110 7 LD = 1 D = 2 When Q(t) = 0 LD = 1 D = 7 When Q(t) = 5 LD = 1 D = 6 When Q(t) = 7 LD = 1 D = 0 When Q(t) = 6 Through K-map, we derive LD = Q2’ Q1’ + Q2Q0 + Q2 Q1 D2 = Q0 D1 = Q1’ + Q0 D0 = Q1’Q0

Cascade Counter A Cascade Modulo 256 Counter Q7,Q6,Q5,Q4 Q3,Q2,Q1,Q0 TC0 CNT LD CNT LD X TC TC Clk Clk D7,D6,D5,D4 D3,D2,D1,D0

Cascade Counter Time 1 2 3 … 13 14 15 16 17 18 19 Q7-4 TC0 Q3-0 TC = 1 when (Q3,Q2,Q1,Q0 )=(1,1,1,1) and X=1 (Q7 (t+1) Q6 (t+1) Q5 (t+1) Q4 (t+1) ) = (Q7 (t) Q6 (t) Q5 (t) Q4 (t) ) + 1 mod 16 when TC0 = 1 The circuit functions as a modulo 256 counter. Time 1 2 3 … 13 14 15 16 17 18 19 Q7-4 TC0 Q3-0