11/21/2023 0 Comments Solved problems on sequential circuits![]() The meaning of this assignment is that both f(x, y, a) and g(x, y, a) are evaluated, and the values are simultaneously assigned to x and y respectively. Since that is all that makes sense if we want to implement the program using fully synchronous hardware. Let's rewrite the loop body so that the state change becomes a single simultaneous assignment of the form Pulling the cord for a second time does just the same thing, but with the roles of 0 and 1 swapped. When the cord is released, x is set to one also, without any change in the output. When you pull the cord, y becomes one, but x stays at zero, and this remains true however long the cord is held. We could try drawing a diagram of states, but we can also see that the following program does the right thing. (If you've used a switch like this, you know there are two clunks – two changes of state – for each pull of the cord.) The arrows on the timing diagram mark two clock edges where the light is on and the input a is 1, but in one case the light stays on, and in the other it goes off. It's tempting to think that this circuit has just two states – on and off – but that's not so. In our digital circuit, the light will switch on the next clock edge following the change in input. The switch has one input and one output: the output changes state just once for each pulse on the input, however long. It stays on when you release the cord, but goes off when the cord is pulled for a second time. The first time you pull the cord, the light comes on. Let's design a digital implementation of the kind of pull-cord light switch that is often found in British bathrooms. ![]() ![]() For the circuit to work correctly we must set the clock period T so that T ≥ t 1 + t 2 + t 3 + t 4, and the same for all combinational paths.Īnother timing calculation, involving contamination delays, is needed to put a bound on the amount of clock skew the circuit can tolerate. In the diagram, time t 1 is the propagation delay of the first flip-flop times t 2 and t 3 are the propagation delays of the two gates, and time t 4 is the setup time of the second flip-flop. ![]() If you search for datasheets of SSI chips, you can find equivalent circuits for flip-flops in terms of gates: but you shouldn't take them too seriously, because the dynamic behaviour of a flip-flop over time cannot be deduced from the static behaviour of a collection of logic gates.īefore we look at the problem of specifying and designing sequential circuits, we should work out the behaviour of a given circuit.ĭelays accumulate along each combinational path. Most flip-flops have an 'asynchronous reset' input that can be used to ensure this. We will assume the initial condition z 0 = 0. (Other kinds of flip-flop exist where the next state depends on the current state as well as the input – they used to be popular with SSI logic, because they sometimes lead to simpler designs.) We could spell out this behaviour in a kind of truth table, though it is a bit boring.Īs you can see, the next state is always the same as the input, whatever the current state might be. The D-type always produces as its output the value that its input had during the previous clock period The little triangle in the circuit symbol means that the state of the flip-flop can change only when the clock signal makes a transition from 0 to 1 – a positive-going clock edge.īecause signals can now change over time, each wire will now carry a sequence of Boolean valuesĬombinational gates compute the same function in each clock period: for an AND gate, We will concentrate on fully synchronous designs where all the clock inputs of flip-flops are connected to a single, regular, global clock signal – perhaps derived from a quartz crystal. The flip-flop has two inputs, d and clk, and one or two outputs, one called q, and perhaps (for convenience) another equal to ¬ q.
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