#### Concept of Sequential Circuit Design, Finite State Machines

Sequential circuit design:

It is a logic design for mod 4 counter. State assignment utilizing Gray codes (each and every transition modifies 1 single bit).

State assignment: 2 Boolean variables x and y code the states: s0: 00, s1: 01, s2: 11, s3: 10.

Input c: count the number of 1’s, avoid 0s. Output b: b = 1 in s3, b = 0 or else.

Combinational logic:  X: = ¬ c ∧ x ∨ c ∧ y, y: = ¬ c ∧ y ∨ c ∧ ¬ x, b: = x ∧ ¬ y

Design a digital watch interface: State space as the Cartesian product

Aim: 2 buttons suffice, no operating manual is required.

This is a state space (which should be) visible to the user, example by displaying the function (example: TZ2) and by flashing active field. The machine’s internal state space obviously is much more complicated. Each field is a counter: mod 12, mod 31, mod 24 and mod 60.

Design principle: The state space visible to user is a homomorphic image of an internal state space.

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