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Mat385 Finite State Machine (Binary Adder)

Andrew E Long
The Binary Adder:

Andy LongSpring, 2020 - Year of Covid-19​
Having constructed a working example of a finite state machine (FSM), from Gersting's 7th edition (p. 730, Example 29), I decided to create a more useful one -- a binary adder (p. 732). It works!
Subject to these rules:
  1. Your two binary numbers should start off the same length -- pad with zeros if necessary. Call this length L.
  2. Now pad your two binary numbers with three extra 0s at the end; this lets the binary-to-decimal conversion execute.
  3. numbers are entered from ones place (left to right).
  4. In Settings, choose "simulation start" as 1, your "simulation length" as L+2 -- two more than the length of your initial input number vectors. (I wish that the Settings issues could be set without having to explicitly change it each time -- maybe it can, but I don't know how.)
Be attentive to order -- start with 1s place, 2s place, 4s, place, etc., and your output answer will be read in the same order.

To understand why we need three additional inputs of 0s:
  1. For the useless first piece of output -- so n -> n+1
  2. For the possibility of adding two binary numbers and ending up with an additional place we need to force out: 111 + 111 = 0 1 1 1
  3. For the delay in computing the decimal number: it reads the preceding output to compute the decimal value.

Computer Science Mathematics Binary Adder Finite State Machine FSM MAT385

  • 1 year 1 month ago

Mat385 Discrete Math FSM -- Recognition

Andrew E Long
One of my favorite topics in Discrete Math is Finite State Machines (FSM). We study deterministic machines without feedback, which can be used to
 * recognize certain types of strings * perform certain tasks (e.g. binary addition).

This particular example of an FSM recognizes input that include multiples of 3 0s (including none). If the nth input represents a complete multiple of 3 0s, then the output will be 1; otherwise 0.

Andy LongSpring, 2020
Year of Covid-19​

Computer Science Mathematics Finite State Machine FSM MAT385

  • 2 weeks 5 days ago