Understanding and Building Different Types of Counters in Digital Logic, Study notes of Computer Architecture and Organization

Download Understanding and Building Different Types of Counters in Digital Logic and more Study notes Computer Architecture and Organization in PDF only on Docsity! Counters 1 Counters • Next, we’ll look at different kinds of counters and discuss how to build them. • These are not only examples of sequential analysis and design, but also real devices used in larger circuits, as we’ll see in the coming weeks. Counters 2 Introducing counters • Counters are a specific type of sequential circuit. • The state, or the flip-flop values themselves, serves as the “output.” • The output value increases by one on each clock cycle. • After the largest value, the output “wraps around” back to 0. • Using two bits, we’d get something like this: • We’ll soon look at some extensions to this basic idea. Present State Next State A B A B 0 0 0 1 0 1 1 0 1 0 1 1 1 1 0 0 00 01 1011 1 11 1 Counters 5 The complete state diagram and table 00 01 1011 0 0 0 10 1 1 1 Present State Inputs Next State Q1 Q0 X Q1 Q0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 0 • Here’s the complete state diagram and state table for this circuit. – Make sure you know how to come up with these – this is a typical sequential design problem! Counters 6 D flip-flop inputs • If we use D flip-flops, then the D inputs will just be the same as the desired next states. • K-maps for the D flip-flop inputs are shown at the right. Present State Inputs Next State Q1 Q0 X Q1 Q0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 0 Q0 0 1 0 1 Q1 1 0 1 0 X Q0 1 1 0 0 Q1 1 1 0 0 X D1 = D0 = Counters 7 D flip-flop inputs • If we use D flip-flops, then the D inputs will just be the same as the desired next states. • Equations for the D flip-flop inputs are shown at the right. • Why does D0 = Q0’ make sense? Present State Inputs Next State Q1 Q0 X Q1 Q0 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 0 Q0 0 1 0 1 Q1 1 0 1 0 X Q0 1 1 0 0 Q1 1 1 0 0 X D1 = Q1 ⊕ Q0 ⊕ X D0 = Q0’ Counters 10 JK flip-flop input equations • J1 = • K1 = • J0 = • K0 = Present State Inputs Next State Flip flop inputs Q1 Q0 X Q1 Q0 J1 K1 J0 K0 0 0 0 0 1 0 x 1 x 0 0 1 1 1 1 x 1 x 0 1 0 1 0 1 x x 1 0 1 1 0 0 0 x x 1 1 0 0 1 1 x 0 1 x 1 0 1 0 1 x 1 1 x 1 1 0 0 0 x 1 x 1 1 1 1 1 0 x 0 x 1 Counters 11 JK flip-flop input equations • We can then find equations for all four flip-flop inputs, in terms of the present state and inputs. Here, it turns out J1 = K1 and J0 = K0. J1 = K1 = Q0’ X + Q0 X’ = Q0 ⊕ X J0 = K0 = 1 • Why does J0 = K0 = 1 make sense? Present State Inputs Next State Flip flop inputs Q1 Q0 X Q1 Q0 J1 K1 J0 K0 0 0 0 0 1 0 x 1 x 0 0 1 1 1 1 x 1 x 0 1 0 1 0 1 x x 1 0 1 1 0 0 0 x x 1 1 0 0 1 1 x 0 1 x 1 0 1 0 1 x 1 1 x 1 1 0 0 0 x 1 x 1 1 1 1 1 0 x 0 x 1 Counters 12 The counter in LogicWorks again • Here is the counter again, but using JK Flip Flop n.i. RS devices instead. • The “n.i. RS” part means that the direct inputs R and S are non-inverted, or active-high. • So this version of the circuit counts normally when Reset = 0, but initializes to 00 when Reset is 1. Counters 15 …or maybe you do care • To get the safest possible circuit, you can explicitly fill in next states for the unused states 110 and 111. • This guarantees that even if the circuit somehow enters an unused state, it will eventually end up in a valid state. • This is called a self-starting counter. Present State Next State Q2 Q1 Q0 Q2 Q1 Q0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 001 010 011 100 101 000 111110 Counters 16 LogicWorks counters • There are a couple of different counters available in LogicWorks. • The simplest one, the Counter-4 Min, just increments once on each clock cycle. – This is a four-bit counter, with values ranging from 0000 to 1111. – The only “input” is the clock signal. Counters 17 More complex counters • More complex counters are also possible. The full-featured LogicWorks Counter-4 device below has several functions. – It can increment or decrement, by setting the UP input to 1 or 0. – You can immediately (asynchronously) clear the counter to 0000 by setting CLR = 1. – You can specify the counter’s next output by setting D3-D0 to any four-bit value and clearing LD. – The active-low EN input enables or disables the counter. • When the counter is disabled, it continues to output the same value without incrementing, decrementing, loading, or clearing. – The “counter out” CO is normally 1, but becomes 0 when the counter reaches its maximum value, 1111. Counters 20 Another restricted counter • We can also make a circuit that counts up to only 1100, instead of 1111. • Here, when the counter value reaches 1100, the NAND gate forces the counter to load, so the next state becomes 0000. Counters 21 Count by 2’s • How might you make the counter count by 2’s? E.g. 0000, 0010, 1110 Counters 22 Summary • Counters serve many purposes in sequential logic design. • There are lots of variations on the basic counter. – Some can increment or decrement. – An enable signal can be added. – The counter’s value may be explicitly set. • There are also several ways to make counters. – You can follow the sequential design principles from last week to build counters from scratch. – You could also modify or combine existing counter devices.