Write $\backslash$graf code for a @tm that computes the one's complement of a binary string. Show the simulation with a string of length $10.$ One's complement is a method of encoding negative numbers. You can compute the One's complement of a binary number as @fllws:

$>[1]$ Flip each bit.

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The @fllwng table shows an encoding @exm for a $4-$bit register:

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:fig table

n $($binary$)$ # n $($decimal$)$ # $-$n $($binary$)$ # $-$n $($decimal$)$

$0000$ # $0$ # $1111$ # $-0$ # $-0!=0$

$0001$ # $1$ # $1110$ # $-1$

$0010$ # $2$ # $1101$ # $-2$

$0011$ # $3$ # $1100$ # $-3$

$0100$ # $4$ # $1011$ # $-4$

$0101$ # $5$ # $1010$ # $-5$

$0110$ # $6$ # $1001$ # $-6$

$0111$ # $7$ # $1000$ # $-7$

done.

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$[$nb$]$ The one's complement on $-$n produces the number n$.$

$[$nb$]$ Only the numbers $-7$ through $7$ can be stored using one's complement with $4$ bits.

$[$nb$]$ One's complement is inconvenient @bc there are $2$ different binary strings that represent $0,$ namely $\backslash [0000]$ and $\backslash [1111].$