CAIS $236-001$

Homework #$6$

Worth $100$ points

Submit

A PDF version of this document with answers provided for problems $1$ through $3.$ If not in PDF$,$ you get a $5$ point deduction.

A Logisim circuit with subcircuits with names as specified in problems $1$ through $3.$

In each of the subcircuits, you must have the following circuit included.

Counter is an $8-$bit counter $($available from Logisim's memory section$)$ that counts up by $1$ for every clock pulse. Your score for each subcircuit will be based on how many clock pulses were needed to finish a given task. In order to accomplish this, each of your subcircuits must use tunnels named CP as source of clock pulses. Also, in order to stop the clock pulses, and hence, the counting by the Counter, each of your subcircuits must include a logic that turns on a tunnel named "Stop CP$"$ when clock pulses are no longer needed.

If you are using a comparator, you must choose "unsigned" for the numeric type property for the comparator since we will be dealing with non$-$negative numbers only.

$($Subcircuit name: Fibonacci$)$ Let an $8-$bit register named curr hold the most recent Fibonacci number generated. Let an $8-$bit register named prev hold the Fibonacci

number preceding curr. Let an $8-$bit counter named fcount hold the number of Fibonacci numbers generated so far. After a Logisim reset, the initial values $($entered manually by the user$)$ is $1($for curr$),0($for prev$),$ and $2($for fcount$).$ Then, the user will start the clock pulse generator. For each clock pulse coming from the label $"$ CP $",$ the curr register must update to the next Fibonacci number, while the prev register updates accordingly, and the fcount counter increments by $1.$ Your circuit must stop updating these registers$/$counters if the current Fibonacci number has reached the maximum Fibonacci number $255.$ Provide answers for the following questions.

a$.(10$ points$)$ Provide the logic formula for the tunnel "Stop CP$".$ If you are using a comparator output, you may use a form like