Establish a convention for representing positive and negative integers in unary

notation. With your convention, sketch the construction of a subtracter for

computing $x-y.$

Using adders, subtracters, comparers, copiers, or multipliers, draw block

diagrams for Turing machines that compute the following functions for all

positive integers $n$ :

$($a$)f(n)=n(n+2).$

$($b$)f(n)=n^4.$

$($c$)f(n)=2^n.$

$($d$)f(n)=n!.$

$($e$)f(n)=2^{n!}.$

Use a block diagram to sketch the implementation of a function $f$ defined for

all $w_1,w_2,w_{3}in\{1{\}}^{+}$by

$f(w_1,w_2,w_3)=i$

where $i$ is such that $|w_i|=$max$(|w_1|,|w_2|,|w_3|)$ if no two $w\text{'}$s have the same

length, and $i=0$ otherwise.