Preparation $($Pre$-$lab$)$

Do the complete paper design for the counter specified in Design I. Your paper design must include the following items:

State transition table for the counter

K$-$maps for each of the flip$-$flop input equations.

Minimized sum of products $($SoP$)$ equation for each flip$-$flop input signal.

Description

In this lab, you will design a unique counter that implements the state diagram shown in the figure below. Each student will be given an individualized count sequence to implement. The count values $x_1-x_6$ shown in the figure will be some sequence of the numbers $1-6,$ with each number used only once. This circuit will simulate rolling a die.

$1$

Figure $1.$ Counter State Diagram

Note that the counter has an input, Rb $,$ which stands for "Roll button". The counter counts as long as $Rb=1,$ but when $Rb=0$ the counter maintains the last count value.

There is one other possible state in a $3-$bit counter design. For example if $x_1$ to $x_6$ correspond to state bits $001$ to $110$ and the reset state corresponds to state bits $000,$ the "missing" state has state bits $111.$ It is possible that the state machine could power$-$up in this state. If so$,$ you must guarantee that the state machine does not remain stuck in this state, even when the reset switch is not pressed. Thus, the next state assignment from the missing state must be to one of the states in the count sequence, $x_1$ to $x_6,$ or the reset state. Sequence is $326154$