How to design a dfa for this problem

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Design a tiny arithmetic unit. It operates with integers between 0 and 15 (inclusive) that can be represented in binary with 4 bits (from 0000 to 1111). The arithmetic unit stores a single such number x that is initially 0000 and should support the following operations:

  • increment: x ← x+1. If the updated value of x exceeds 15 then x wraps around and becomes 0.
  • decrement: x ← x-1. If the updated value of x drops below 0 then x wraps around and becomes 15.
  • division by 2: x ←bx 2c.
  • multiplication by 2 : x ← 2x. If the updated value of x exceeds 15 then x wraps around and becomes 2x-16.

How to Design a DFA for this problem?

Reference no: EM132400921

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