Write $\backslash$graf code for a @tm that computes the two's complement of a binary string. Show the simulation with the strings $\backslash [0100]$ and $\backslash [1100].$ Two's complement

$>$ The two's complement method is a modification of one's complement that fixes the problem of there being two different binary numbers representing $0.$ You can compute the two's complement of a binary number as @fllws:

$>[1]$ Compute the one's complement

$>[2]$ Add $1$

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$>$ Below is a table showing the two's complement encodings for a $4-$bit register:

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:fig table

n $($binary$)$ # n $($decimal$)$ # one's complement # $-$n $($binary$)$ # $-$n $($decimal$)$

$0000$ # $0$ # $1111$ # $!\{1\}0000$ # $0$

$0001$ # $1$ # $1110$ # $1111$ # $-1$

$0010$ # $2$ # $1101$ # $1110$ # $-2$

$0011$ # $3$ # $1100$ # $1101$ # $-3$

$0100$ # $4$ # $1011$ # $1100$ # $-4$

$0101$ # $5$ # $1010$ # $1011$ # $-5$

$0110$ # $6$ # $1001$ # $1010$ # $-6$

$0111$ # $7$ # $1000$ # $1001$ # $-7$

done.

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$[$nb$]$ The two's complement of $-$n produces n$.$

$[$nb$]$ The two's complement of $\backslash [0000]$ overflows the register, leaving only $\backslash [0000].$