ECE/EEE/INSTR F215 DIGITAL DESIGN Tushar Sakorikar Synchronous Up-down counter Count up 1 Count down A3 A2 A1 A0 A3 A2 A1 A0 0 0 0 0 1 1 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 Synchronous BCD counter Present State Flip Flop inputs Next State o/p Q8 Q4 Q2 Q1 Q8 Q4 Q2 Q1 T8 T4 T2 T1 Y 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 0 1 1 1 0 0 1 0 0 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 0 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 1 Flip Flop I/P Equations • T1 = 1 • Solve for K-maps and get these equations. • Minterms 10 to 15 are taken as don’t‐care terms • T2 = Q’8 Q1 • T4 = Q2 Q1 • T8 = Q8 Q1 + Q4 Q2 Q1 • Y = Q8 Q1 Registers Register with parallel load 2:1 Mux Shift register Shift register Serial Transfer Serial Addition Serial Addition e.g. Using Shift registers and J-K Flip Flop Cin Cout Serial Addition e.g. Using Shift registers and J-K Flip Flop Universal Shift Register 4-bit binary counter with parallel load 4-bit binary counter with parallel load • Load = 1: Counter disabled and register enabled • Count=1 and Load =0: Counter is enabled and register disabled • Load and Count = 0: J and K are 0, Clk pulses do not change the state of register BCD counter using a counter with parallel load Counter with Unused States • To simplify the Flip Flop I/P equations, the unused states may be treated as don’t‐care conditions or may be assigned specific next states. • Care must be taken to ensure that in case the circuit goes into one of the unused states, there is a way out to get it back into the valid states to resume normal operation. How to make sure? After the circuit is designed, make sure to check the effect of counter going in one of the unused states. Counter with Unused States It excludes: 111 and 011 Counter with Unused States Ring Counter Johnson Counter DC What happens if it goes into a unused state? It keeps moving from 1 unused state to other! To correct this error: DC= (A+C)B (work it out to check if it solves the problem!) Johnson Counter Applications 1. Davies Generator Generates stepped sinusoid O/P 2. Frequency Divider 3. Pattern Recognition