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Mealy Machines part 2

Mealy Machines part 2. Adder as a Mealy machine. Two states Alphabet is set of pairs Every transition emits an output character Emits the sum of the two numbers formed where each bit is paired together (least signifcant bits first) 0 01 + 111 uses input (1,1)(0,1),(0,1).

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Mealy Machines part 2

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  1. Mealy Machines part 2

  2. Adder as a Mealy machine • Two states • Alphabet is set of pairs • Every transition emits an output character • Emits the sum of the two numbers formed where each bit is paired together (least signifcant bits first) • 001 + 111 uses input (1,1)(0,1),(0,1)

  3. For a fixed number of bits (here we use 4) we can unfold the machine. • The length of a path to the accepting state is a function of the number of bits (4+1) • Can we do better? • trade shorter path length for more states?

  4. This is exactly analagous tothe Ripple Carry Adder 0 1 0 1 0 1 1 0 1 0 1 1 1 0 1 1

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