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Counters

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**Asynchronous and Synchronous Circuits**

Consider the timing diagram for the 4-bit counter circuit. There is a delay or ripple effect on the output transitions, each output being delayed from the previous due to the propagation delay through the flip-flop. When all the outputs do not become valid “at once”, the circuit is ASYNCHRONOUS. These circuits are generally identified by the different flip-flops being clocked by different signals. This counter circuit is often called a RIPPLE COUNTER. Valid Output Clock Q0 Q1 Q2 Q3

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Synchronous Circuits In many circuits it is necessary to ensure that all outputs change simultaneously or SYNCHRONOUSLY. This can be achieved by clocking all the flip-flops with the same clock signal. Look at a Synchronous 4-bit counter circuit This circuit must produce synchronous outputs because all the flip-flops are clocked by the same signal. D Q C0 Q0 C1 Q1 C2 Q2 C3 Q3 Clock

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**Synchronous Counter: A Closer Look**

To look at how this might work, we will first simplify it to a 2-bit counter, ie: 00->01->10->11->00->… At startup the outputs are both 0. These feed back into the comb. cct to put values of 1 for Y0 and 0 for Y1, ready for the next clock pulse. The clock “strikes”: the 1 and 0 flow through to X0 and X1, but again feed back to the comb. cct which places 0 onto Y0 & 1 onto Y1 (ready for the next clock). The clock “strikes”: the 0 and 1 flow back to the combinatorial circuit which places 1 onto Y0 & 1 onto Y1. The clock “strikes”: the 1 and 1 flow through to X0 and X1, but again feed back to the combinatorial cct which places 0 onto Y0 & 0 onto Y1. Clock: The X’s are both 0 & the Y’s are 1 & 0, we’re back to the start. X0 X1 Clock Combinatorial Circuit Y0 Y1

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**Synchronous Counter as a State Machine**

How is this counter working? The outputs are part of the inputs for the next Y0 and Y1 pair, ie the circuit is remembering its past output. That is, it’s behaving like a state machine. Sometimes it is better to model the behaviour of a machine rather than what it actually looks like. The PALASM system allows us to specify a machine as a state machine and it will program the circuits for us. So that is the direction we must now take: State Machines and The PALASM System Section 3. S0 00 S1 01 S2 10 S3 11 X1 X0

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Sequential Circuits Problems(I) Prof. Sin-Min Lee Department of Mathematics and Computer Science Algorithm = Logic + Control.

Sequential Circuits Problems(I) Prof. Sin-Min Lee Department of Mathematics and Computer Science Algorithm = Logic + Control.

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