Why ASM

• A digital system often has a data path which is controlled by a finite state m/c serving as the controller
• A state m/c representation may be rather cumbersome when there are a large number of inputs and outputs
• Compared to a state diagram, it's a flowchart based representation of the sequence of operations to be carried
• Offers the advantage of not requiring the listing of all input conditions and possible output conditions
• Example of some digital systems where the controller may be represented via ASM: multiplier for unsigned integers, Booth's multiplier, floating point adder

ASM chart

• It depicts links between the various operations that need to be carried out
• Three types of symbols used in ASM charts are as follows:
  1. a rectangle is used to represent outputs not dependent on input conditions, such as the flip-flop outputs
  2. a diamond or hexagon is associated with conditional execution of operations; for n inputs, 2ⁿ branches are possible
  3. a rectangle with rounded corners is used to yield the conditional outputs (dependent on inputs)
  
• Circuits associated with the ASM symbols are depicted next
• Section of an ASM chart and corresponding logic circuits are shown
• Caution needs to be exercised to avoid races; figure (a), below, admits races and should be avoided
• An ASM chart and its associated Moore m/c is shown next
• In this ASM chart, note that all joins are from mutually exclusive branches of computation
• The ASM chart fragment shown next admits concurrency
• The tests on X and Y can be done concurrently
• However, the concurrent branches need to join subsequently, as indicated
• Joining using an OR gate will not be adequate, instead an AND gate may be used to synchronise the concurrent brances, if the inputs remain steady
• If not, a Muller-C element (not covered) should be used

Serial adder example

Serial adder data path

Serial adder ASM chart

Exercises

• Formulate the datapath for a transmitter for an Hamming SECC for four data bits (and three parity bits) and the ASM chart for the associated controller
• Formulate the datapath for a receiver for an Hamming SECC for four data bits (and three parity bits) and the ASM chart for the associated controller
• Note that there is scope for parallelism for both parity bit generation and error correction; that should be accommodated in the design of your ASM charts (Muller-C element will not be needed)