What is the purpose of the sign bit in sign-magnitude representation? Provide examples of two 8 bit sign-magnitude numbers, one positive and the other negative.

Explain how to perform twos complement representation and convert -6 to twos complement representation.

What is overflow and when does it occur?

Why is biased representation used for the exponent in floating point numbers?

What is rounding?

Write the decimal values 23 and -23 in binary sign-magnitude representation.

Write the following decimal values in twos complement representation using 8 binary bits: -15 and -32.         

Add decimal 10 to decimal -5 using twos complement and present the result in 8 binary bits.               

Represent the following decimal numbers in IEEE floating point representation: 25.5 and - 8.0.

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The leftmost bit which is used for sign helps figuring if we deal with a positive number or a negative number. If the number is positive, the sign bit is 0, otherwise, if it is 1, then the number is negative. For example, -25 in signed-magnitude 8-bit binary is: 1001 1001, while +7 in the same representation is 0000 0111....

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