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CS 60

Finite-State Machines Worksheet

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1. Simulate the following machine for input 11101100. What is the output?

2. Present the next-state and output tables for the machine above.

3. Draw the state-transition diagram for a machine which outputs the modulo-2 sum of the last two digits of input. For example:

start

input: 0 1 1 0 1 1 1 1 0 0

output: 0 1 0 1 1 0 0 0 1 0

4. Draw the state-transition diagram for a machine which adds 2 binary numerals, LSB first. The input bits are provided pair wise :

5. Draw the state-transition diagram for a machine which computes the maximum of 2 binary numerals, aligned MSB first:

6. Draw the state-transition diagram for a machine which multiplies its binary input LSB first by 2

7. Draw the state-transition diagram for a machine which multiplies its input LSB first by 3

              start
              v
    0 0 1 1 0 1 } input
    1 0 0 1 1 1 } output

8. For the example below, construct a logic realization using the state encoding {00, 01, 10} for {0, 1, 2} respectively.

9. For the preceding example, give the logic equations for the next state variables assuming a one-hot encoding.