Differences between signed and unsigned decimal values What are examples of signed and unsigned decimal values?  What are the differences between them?
 A: Computers used a set of bits to represent numbers.  Signed and unsigned numbers are two different ways of mapping bits to numbers.  Here is an example for 8 bits:
$$\begin{array} {c|c|c}
\text{Bits} & \text{Unsigned Number} & \text{Signed Number} \\ \hline
0000\,0000 & 0 & 0 \\
0000\,0001 & 1 & 1 \\
0000\,0010 & 2 & 2 \\
0000\,0011 & 3 & 3 \\
\vdots & \vdots & \vdots \\
0111\,1110 & 126 & 126 \\
0111\,1111 & 127 & 127 \\
1000\,0000 & 128 & -128 \\
1000\,0001 & 129 & -127 \\
\vdots & \vdots & \vdots \\
1111\,1110 & 254 & -2 \\
1111\,1111 & 255 & -1 \\
\end{array}$$
Suppose an unsigned number $U$ and a signed number $S$ have the same $n$ bit pattern.  Then notice that:
$$U \equiv S \pmod{2^n}$$
As a result, $A + B \pmod{2^n}$, $A - B \pmod{2^n}$, and $A \times B \pmod{2^n}$, can be computed the with the same circuit regardless of whether $A$ and $B$ are signed or not.
The differences between signed and unsigned numbers occur when:


*

*Converting the bit pattern to a string (you have to know whether a number is signed or not to correctly print the value of $1111\,1110$, for example)

*Comparing two values: which is larger, $0111\,1111$ or $1000\,0000$? It depends on whether they are signed or not

*Division

*Sometimes a signed bit shift to the right is preferred to pad the left with the MSB rather than with zero

A: A signed value uses one bit to specify the sign (i.e. $-$ or $+$) whereas an unsigned value does not.
For example, $-127$ and $+127$ are both signed while $255$ and $0$ are unsigned.
A: Consider an 8 bit value like that:
b7 b6 b5 b4 b3 b2 b1 b0

If this value is unsigned you cannot express negative values. Therefore, you can only express values between $0$ and $2^8-1=+255$. (If you use n bits then this range is between $0$ and $2^n-1$)
If this value is signed then b7 bit is used to determine the sign and you can express negative values. The value of the expressed number is positive if b7 is $0$ and negative if b7 is $1$. Since you are using one bit to determine the sign, you have to express values using 7 bits (b6...b0). Therefore the range is between $-2^7$ and $+2^7-1$.
For example:
"00001001"=+9
You should know 2's complement to express -9
"10111000"=-9
However, if you use unsigned notation then "10111000"=+184.
I hope you understand.
