CmpSci 535 Discussion 8
Sequential Circuits
We can build a minimal
sequential circuit by cross-coupling the outputs of two gates to each other's
inputs. This forms a feedback loop that snaps into one state or another given
particular inputs, and holds this state after the inputs are removed. The
circuit is a single-bit memory known as a flip- flop.
The simple flip flop of this
form is called an S-R (set-reset) flip-flop because its output is set to one
when one of its inputs is 1 and the other is 0, and when the opposite
combination of inputs is applied the output becomes 0.
Note that 0-0 is an input
that causes an invalid output state. We can gang up a bunch of flip-flops to
form a register. However, we want to be able to load all of the bits of the
register together using multiple input lines but a single control line. How
might we do this? Feed the control line to NAND gates at the inputs of the
flip- flops. When the control is low, the inputs are applied (inverted) to the flip-flops.
When it is low, they see 1. We have to invert the meaning of the inputs to
compensate (the top becomes the Set input, and the bottom is Reset in the above
diagram.)
If we feed one of the inputs
through an inverter and an OR gate (see discussion 9 for a diagram) to the
other input we get a flip flop that stores its input value when the control
signal is applied -- also called a latch or D flip-flop. The D flip-flop is
just what we need to build a register. However, it has the nasty property that
whenever the control line is high, changes in the input all go through to the
output. This could lead subsequent circuitry to produce temporary erroneous
results.
The solution is to gang two
flip flops in series with the control signal going to the second of them
inverted. The result is that when the control signal goes low, the second flip
flop holds its value while the first one tracks the input. Then, when the
control signal goes high again, the first flip-flop locks its value down and
the second flip flop takes this final value as its input. Thus, only the one
change is seen to occur at the output. The control signal is usually called the
clock. Flip flops like this are called master-slave. They can be ganged in
series to form a shift register, or in parallel to form a normal register.
A block of N registers can be
assembled to form a register file, and a decoder circuit can be provided that
takes a log N input register number and outputs a signal to select the given
register (selection is simply the ANDing of this signal with the clock input to
the particular register).
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