Page 157 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

138 Chapter Twelve

program can be used to obtain the same results in less time with far fewer
opportunities for error.6 Whichever technique is employed, the state
assignments above lead to the following minimized Boolean equations:

dO = (T & $& dime) I (40 & 42 & nickel) I (010 & nickel)
-_.
dl = (qO&q2&dime)
I
&
d2 = (q0 & F) (42 & niGkel& dime) I (q 42 & dime)
dispense = (qO&q)
change = (ql)

The product terms shown in bold appear in multiple equations. However,
regardless of the number of times a product term appears, it is only counted
once because it only has to be physically implemented once. Similarly, the
literals used to form product terms that appear in multiple equations are only
counted once.
Another common form of state assignment is known as one-hot encoding,
in which each state is represented by an individual register. In this case, our
controller with its five states would require five register bits. The one-hot

technique typically requires a greater number of logic gates than does binary
encoding. However, as the logic gates are used to implement simpler equations,
the one-hot method results in faster state machines that can operate at higher

clock frequencies,

Don’t Care States, Unused States, and Latch-Up Conditions

It was previously noted that the analysis of the binary encoded state
assignment made full use of don’t cure state^.^ This allows us to generate a
solution that uses the least number of logic gates, but there are additional
considerations that must now be discussed in more detail.
The original definition of our coin-operated machine stated that it is only
possible for a single coin to be deposited at a time. Assuming this to be true,

6 Once again, the author used BOOL (“What’s the point of barking if you have a dog?” as they say
in England).
7 The concept of don’t care states was introduced in Chapter 10.