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introduction_to_digital_systems:number_systems [2023/11/09 20:34]
mexleadmin [Exercises] 		introduction_to_digital_systems:number_systems [2023/11/16 01:08]
mexleadmin
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                +672 \\                +672 \\
 \hline  \hline 
-1\overset{\color{red}{2}}{1}\overset{\color{red}{1}}{4}\overset{}{2}+1\overset{\color{red}{2}}{2}\overset{\color{red}{1}}{4}\overset{}{2}
 \end{align*} \end{align*}
  
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 </WRAP></WRAP></panel> </WRAP></WRAP></panel>
  
-<panel type="info" title="Exercise 2.3.9. One's Complement"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>+<panel type="info" title="Exercise 2.3.9. Two's Complement"> <WRAP group><WRAP column 2%>{{fa>pencil?32}}</WRAP><WRAP column 92%>
  
-In the simulation in <imgref pic70> the one's complement of a 4bit value is shown. \\ +In the simulation in <imgref pic70> the two's complement of a 4bit value is shown. \\ 
-On initialization the value is the following:  +On initialization, the value is the following: 
-  * The value for $A$ is $1010_2 = 10_{10}$. The decimal value ''10'' is also shown in the first display from the left in the circuit.  +  * The value for variable $A$ is $1010_2 = 10_{10}$. The decimal value ''10'' is also shown in the first display from the left in the circuit.  
-  * The value for $B$ is $1110_2 = 14_{10}$. The decimal value ''14'' is also shown in the second display from the left in the circuit.  +  * The value for variable $B$ is $1110_2 = 14_{10}$. The decimal value ''14'' is also shown in the second display from the left in the circuit.  
-  * The addition $A+B$ leads to $S = 1000_2 = 8_{10}$. The decimal value ''10'' is also shown in the rightmost display in the circuit.  +  * The addition $A+B$ leads to $S = 1000_2 = 8_{10}$. The decimal value ''10'' is also shown on the rightmost display in the circuit.  
-  * There is another value in the second display from the right. This is called $B'$ and it is equal to $0010_2 = 2_{10}$.+  * There is another value in the second display from the right. This is called $B'$, and it is equal to $0010_2 = 2_{10}$.
    
 <WRAP><well> <WRAP><well>
-<imgcaption pic70|One's Complement></imgcaption> \\+<imgcaption pic70|Two's Complement></imgcaption> \\
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 </well></WRAP> </well></WRAP>
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   - Why is ''10'' + ''14'' = ''8''? What happens to other values? \\ The input values ''A'' and ''B'' can be changed by clicking on the bit values.    - Why is ''10'' + ''14'' = ''8''? What happens to other values? \\ The input values ''A'' and ''B'' can be changed by clicking on the bit values. 
   - Try to analyze how ''B''' (shown in the brackets) is derived from ''B''.    - Try to analyze how ''B''' (shown in the brackets) is derived from ''B''. 
-  - Have a look at the wiki page of the {{wp>Ones' complement}} to understand how negative numbers are represented in a microcontroller.+  - Have a look at the wiki page of the {{wp>Two's complement}} to understand how negative numbers are represented in a microcontroller. \\ What does the following representation show? \\{{drawio>introduction_to_digital_systems:SignedIntCircle.svg}}
   - Imagine that you have to rescue data from an old storage device. The interesting bits are given by the boxed area in <imgref picex01>. The bytes are LSB 0 oriented.    - Imagine that you have to rescue data from an old storage device. The interesting bits are given by the boxed area in <imgref picex01>. The bytes are LSB 0 oriented. 
     - What are these values in an unsigned integer?     - What are these values in an unsigned integer?
-    - What are these values in signed integers based on the ones' complement? +    - What are these values in signed integers based on the Two's complement?