CSE $221-$ Principles of Logic Design $-2024$ Spring

Homework $2$

You will use a "key" to solve the questions in this homework. The key is the number formed by

the last two digits of your student id$.$ If your key is less than $20,$ add $20$ to it$!($So for example,

if your student id was $20100702047$ your key would be $"47"$; if your student id was

$20100702008$ your key would be $"28".)$ We will assume that the key is $47$ while explaining the

questions $($you should replace it with your own key$).$

So$,$ first write down your id and key: Student Id: $................$ Key: $......$

$(10$ p$)$ Write your first name in lowercase letters $($Example: ali$).($If you have two names, use

only the first one; for Turkish characters use the corresponding English characters: $->$s$,->$g

etc.$)$ Find the ASCII code for your name; use hexadecimal notation. $($ali: $616$C $69)$ Then, do

the same with your name in capital letters. $($ALI: $414$C $49)$

Name $($lowercase$)$: $................$ ASCII Code: $.........................$

Name $($CAPITAL$)$: $.................$ ASCII Code: $.........................$

key mod$6$ If $m$ is odd, add $1$ to it$.(m=8)$

Find your $m.,m=$dots.mod$6+3=$dots $($if odd, then add $1m=$dotsdots $)$

Design a self$-$complementing coding system to represent the digits in base $"m"$ numbering system. For

a code system to be "self$-$complementing", the number obtained by complementing each bit of the

original code of a number should be equal to $r-1\text{'}$s complement of the original number.

$($For example, for base $4$ numbering system, let's say digit $1$ has the code $"001"$ and digit $2$

has the code $"110".$ Then the code for $(11)4$ is $"001001".$ When we complement each bit, we

obtain $"110110"$ and this is the code for $(22)4.22$ is the $3\text{'}$s complement of $11.)$

Write down the codes for your digits on the table below. On the right of the table, give a

partial proof that your code is self complementing: Take a $3-$digit number in base $m$ as an

example, write down its code, then complement this code and show that it is $m-1\text{'}$s

complement of the original number.

Example $3-$digit number $p$ :

Code of $p(C_p)$ :

Complemented Code $C_r$ :

$C_r$ is the code of $(r)$ :

$p+r=$