$1$ Sequential Circuit Design

$1\mathrm{.}1$ Background

There is a game called Screwball. Every time a ball is put in play, either player $1$ scores a point or player $2$ scores a point. A winner is declared when one player is ahead by $2$ points. Starting with a score of $0$:$0$ for $P_1$ vs$.P_2,$ a game might progress as follows: $0$:$0,0$:$1,1$:$1,1$:$2,1$:$3$:$P_2$ wins.

$1\mathrm{.}2$ Problem Description

Your task is to develop a synchronous sequential machine that uses information about which player scores a point at each game stage to indicate BOTH when a player wins and which player wins. Your design should include one reset input to initialize your WIN ANNOUNCER $($this may be a synchronous or asynchronous input as you desire$).$ The outputs from your design should indicate BOTH when a win has occurred and which player is the winner. You are required to follow the typical procedure for sequential circuit design. Implement the design on Logisim and verify its functionality.

$1\mathrm{.}3$ Inputs

The circuit is expected to receive two inputs. If the first input is zero, $P_1$ wins this round, while one means that $P_2$ wins the round. The second input is the reset; no reset is invoked if the reset is zero, while one refers to system reset.

$1\mathrm{.}4$ Outputs

The circuit is expected to generate two outputs; the first output declares a winner. The second output refers to the winning player; zero means that the first player is the winner, while one means that the second player is the winner.

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$2$ Bubble Sort using MARIE Emulator

Assume an array of length $10$; you are required to write a high$-$level code in your preferred language that implements the bubble sort algorithm. Assemble the code for MARIE architecture. Verify the correctness of your implementation using a MARIE emulator.