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introduction_to_digital_systems:number_systems [2023/09/19 23:44] mexleadmin |
introduction_to_digital_systems:number_systems [2023/11/16 01:08] mexleadmin |
+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> |
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<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%> |
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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 $0010_2 = 2_{10}$. |
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<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? |
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