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Optimizing Mealy Machines for Adders | Unfolding the Ripple-Carry Adder

Explore efficient design strategies for Mealy machines representing adders, using pairs of bits and emitting sum outputs. Discover the trade-off between path length and state count applying to fixed-bit calculations like 001 + 111, unfold the machine and ponder alternative enhancements.

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Optimizing Mealy Machines for Adders | Unfolding the Ripple-Carry Adder

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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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