# Question $9(20$ pt$.)$ Design a $4-$bit up$/$down counter. Specifically, there is a button to toggle the circuit's count up$/$down behavior.

Hint: Use the counter like what was learned in the class, then add a Multiplexer with $1-$bit selection for constants $1$ and $-1(1111,$ in $4-$bit two's complement form$).$

Instruction: For this exercise, please complete the work in Logisim Evolution and submit your Logisim file.

Test cases:

Case $1.$ Count Up

Step $1.$ Down $=0$

Step $2.$ Toggle the clock on $(1$ time$),$ the output should be $1$

Step $3.$ Toggle the clock off then on $(1$ time$),$ the output should be $2$

Step $4.$ Toggle the clock off then on $(1$ time$),$ the output should be $3_{{?}_{?}}$

Step $5.$ Toggle the clock off then on $(1$ time$),$ the output should be $4_{?}$

Step $6.$ Toggle the clock off then on $(1$ time$),$ the output should be $5_{{?}_{?}}$

Step $7.$ Toggle the clock off then on $(1$ time$),$ the output should be $6_{{?}_{?}}$

Step $8.$ Toggle the clock off then on $(1$ time$),$ the output should be $7_{{?}_{?}}$

Step $9.$ Toggle the clock off then on $(1$ time$),$ the output should be $8_{?}$

Step $10.$ Toggle the clock off then on $(1$ time$),$ the output should be $9_{?}$

Case $2.$ Count Down

Steps $1$ to $10$ as Case $1$ to bring the value up to $9($if you haven't done so$)$

Step $11$: Down $=1$

Step $12.$ Toggle the clock off then on $(1$ time$),$ the output should be $8_{?}$

Step $13.$ Toggle the clock off then on $(1$ time$),$ the output should be $7_{?}$

Step $14.$ Toggle the clock off then on $(1$ time$),$ the output should be $6_{{?}_{?}}$

Step $15.$ Toggle the clock off then on $(1$ time$),$ the output should be $5_{?}$

Step $16.$ Toggle the clock off then on $(1$ time$),$ the output should be $4$

Step $17.$ Toggle the clock off then on $(1$ time$),$ the output should be $\frac{3}{2}$

Step $18.$ Toggle the clock off then on $(1$ time$),$ the output should be $2$

Step $19.$ Toggle the clock off then on $(1$ time$),$ the output should be $1_{?}$

Step $20.$ Toggle the clock off then on $(1$ time$),$ the output should be $0_{{?}_{?}}$