Design a TM to execute programs written in a simplified assembly$-$like language. Needs to be in the format of the picture.

There are just four instructions: L$,$ Mx$,$ My$,$ and A operating on three registers x$,$ y$,$ and z each

holding a nonnegative integer.

$$ L instructions load a certain constant number, represented in binary, into register z$.$

For example, the instruction L$00000101$ loads the integer $5($represented by the bits

$00000101)$ into z$.$ Other bit strings can be specified. The number of bits may be

arbitrary, but you may assume it is the same for all load instructions in the program. For

instance, if the first instruction is L$0011001100110011,$ then all remaining L instructions

will be followed by exactly $16$ bits.

$$ Mx and My instructions move the value from z into x or y$,$ respectively. $($Actually$,$ it$$s

more like $$copy$$ since the value in z is not erased, but $$move$$ is the traditional assembly

language name for this instruction.$)$

$$ A instructions add the values in registers x and y and store the result in register z$.$ If

the result overflows, the new most significant $1$ is simply omitted; i$.$e$.,$ the result is taken

mod $2$k$,$ where k is the number of bits specified in the first load instruction. For example,

adding $11111111(255)$ to $00000001(1)$ results in $00000000(0),$ and adding $11111010$

$(250)$ to $00001001(9)$ results in $00000011(3).($This might sound difficult, but actually

the straightforward way to implement addition will automatically achieve this.$)$

If an instruction needs to read a register $($add must read x and y$,$ and move must read z$),$

then you may assume that register has already had a value written to it$.$

The input will be a $$ followed by a list of instructions, each followed by a :$,$ such as

$^$L$00000110$:Mx:L$00000111$:My:A:Mx:L$00001001$:My:A:

The above program does the following

$$ load the value $6$ into z and then move it into x$,$

$$ load the value $7$ into z and then move it into y$,$

$$ add x and y and store the result $(13)$ in z$,$

$$ move the value in z $(13)$ into x$,$

$$ load the value $9$ into z and move it into y$,$

$$ add x and y and store the result $(22)$ in z$.$

Your TM should produce a string output equal to the value of register z $($represented as a

binary string$)$ after the last instruction executes. So the correct output above is $00010110.$

Furthermore, your TM should halt in the accept state.

You may assume only input strings matching the above description will be supplied. $($Your

TM does not have to detect syntax errors in the assembly language program.$)$

Hint: It helps to use one worktape per register, and to write special marker symbols at the

start of each of them to help identify when the tape head is scanning the leftmost tape cell.

It is also recommended to use wildcards in the transition rules.