Modulo-4 Up-Down Counter - Lecture Slides | CPSC 5155U, Study notes of Computer Architecture and Organization

Download Modulo-4 Up-Down Counter - Lecture Slides | CPSC 5155U and more Study notes Computer Architecture and Organization in PDF only on Docsity! CPSC 5155 Chapter 7 Slide 1 Modulo–4 Up–Down Counter This is a counter with input. If X = 0, the device counts up: 0, 1, 2, 3, 0, 1, 2, 3, etc. If X = 1, the device counts down: 0, 3, 2, 1, 0, 3, 2, 1, etc. Step 1a: Derive the state diagram and state table for the circuit. Note two transitions between the state pairs: one is up and one is down. Slide 1 of 14 slides Design of a Mod-4 Up Down Counter February 13, 2006 CPSC 5155 Chapter 7 Slide 2 Step 1b: Derive the State Table Present State Next State X = 0 X = 1 0 1 3 1 2 0 2 3 1 3 0 2 This is just a restatement of the state diagram. Note: Two columns for the “Next State”. Slide 2 of 14 slides Design of a Mod-4 Up Down Counter February 13, 2006 CPSC 5155 Chapter 7 Slide 5 Step 4: Derive the state transition table and the output table. There is no computed output, hence no output table. The state transition table uses the 2–bit state vectors Present State Next State X = 0 X = 1 0 00 01 11 1 01 10 00 2 10 11 01 3 11 00 10 Slide 5 of 14 slides Design of a Mod-4 Up Down Counter February 13, 2006 CPSC 5155 Chapter 7 Slide 6 Step 5:Separate the state transition table into P tables, one for each flip-flop. Flip–Flop 1 Flip-Flop 1 PS Next State: Y1 Y1Y0 X = 0 X = 1 0 0 0 1 0 1 1 0 1 0 1 0 1 1 0 1 Flip–Flop 0 Flip-Flop 0: Y0 PS Next State Y1Y0 X = 0 X = 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 Slide 6 of 14 slides Design of a Mod-4 Up Down Counter February 13, 2006 CPSC 5155 Chapter 7 Slide 7 Step 6: Decide on the types of flip-flops to use. When in doubt, use all JK’s. Here is the excitation table for a JK flip–flop Q(T) Q(T+1) J K 0 0 0 d 0 1 1 d 1 0 d 1 1 1 d 0 Slide 7 of 14 slides Design of a Mod-4 Up Down Counter February 13, 2006 CPSC 5155 Chapter 7 Slide 10 Input Equations for Flip–Flop 1 X = 0 X = 1 Y1Y0 Y1 J1 K1 Y1 J1 K1 0 0 0 0 d 1 1 d 0 1 1 1 d 0 0 d 1 0 1 d 0 0 d 1 1 1 0 d 1 1 d 0 J1 = Y0 J1 = Y0’ K1 = Y0 K1 = Y0’ Apply the “combine rule” J1 = X’Y0 + XY0’ = X  Y0 K1 = X’Y0 + XY0’ = X  Y0 Slide 10 of 14 slides Design of a Mod-4 Up Down Counter February 13, 2006 CPSC 5155 Chapter 7 Slide 11 Input Equations for Flip–Flop 0 X = 0 X = 1 Y1Y0 Y0 J0 K0 Y1 J0 K0 0 0 1 1 d 1 1 d 0 1 0 d 1 0 d 1 1 0 1 1 d 1 1 d 1 1 0 d 1 0 d 1 J0 = 1 J0 = 1 K0 = 1 K0 = 1 Apply the “Combine Rule” J0 = X’1 + X1 = 1 K0 = X’1 + X1 = 1 Neither J0 nor K0 depend on X. But Y0 does not depend on X. Slide 11 of 14 slides Design of a Mod-4 Up Down Counter February 13, 2006 CPSC 5155 Chapter 7 Slide 12 Step 9: Summarize the equations by writing them in one place. Here they are. J1 = X  Y0 K1 = X  Y0 J0 = 1 K0 = 1 Slide 12 of 14 slides Design of a Mod-4 Up Down Counter February 13, 2006