next up previous contents index

[ENGN3213 Home]

Example - Up/Down/Stop Counter

Here is the next state/output table for the up/down/stop counter example:

Present state next state   output Y
  up down stop  
s1 s2 s4 s1 odd
s2 s3 s1 s2 even
s3 s4 s2 s3 odd
s4 s1 s3 s4 even

Compare this with the state diagram.

  There are four states, so we need a minimum of two flip flops for the memory, which we label as AB. There are three input values, which we code using two bits SM, and two output values, coded with one bit labeled y.

Let's use the following binary coding:

state AB input SM output y
s1 00 up 00 odd 0
s2 01 down 01 even 1
s3 11 stop 1X    
s4 10        
There are many other possibilities; it is important to know that the choice of coding can have a significant impact on performance and reliability.

With this coding, the next state/output table becomes:

Present state next state   output
  up down stop  
AB S=0,M=0 S=0,M=1 S=1 y
00 01 10 00 0
01 11 00 01 1
11 10 01 11 0
10 00 11 10 1

The general form of the circuit diagram for the state machine is shown in Figure 69. Here we have selected rising edge triggered D flip flops with asynchronous preclear as the memory elements.

Figure 69: Up/down/stop counter circuit diagram.

The RESET signal is set up to force the state machine into a specified state, viz. s1=00.

Our job now is to work out the combinational logic required for the next state and output logic. To do this, we use k-maps, Figure 70.

Figure 70: Up/down/stop counter synthesis k-maps.

We have used SM as entered variables. The k-map squares correspond to the four states (the k-maps are indexed by the state variables AB), and entries are obtained by a consideration of what the next state will be (from the next state table), and making use of the state transition table for the D flip flop.

The result is:

D_A & = \overline{S} . M . \overline{B}
+ \...
...+ \overline{S} . M . A
+ S . B \\
y & = A \oplus B

next up previous contents index

[ENGN3213 Home]

ANU Engineering - ENGN3213