Prove that, for all $n \geq 1$, $|\set{s \in \bit^n : K(s) < n}| \leq 2^n-1$, i. e.\ there are at most $2^n-1$ binary strings of length $n$ that have Kolmogorov complexity strictly less than $n$.

Write a new lc-3 trap subroutine (i.e. a subroutine that will be invoked via the trap instruction) that will receive a numeric digit entered at the keyboard (i.e. an ascii character), echo it to the screen, and return in r0 the corresponding numeric value: so if the user types the digit '7', the character '7' will appear on the screen, but the value returned in r0 will be b0000 0000 0000 0111 (#7) you may not use any trap calls in your code - you must implement the "polling" code that interrogates the keyboard status and data registers. ; getnum_tsr ; a subroutine for obtaining a numeric value ; given ascii numeric digit input to keyboard. ; the numeric digit is echoed to the console (e.g. '7' = b0000 0000 0011 0111), ; but the value returned in r0 is the actual numeric value ; corresponding to the digit (e.g. b0000 0000 0000 0111 =