Sign-Magnitude Number Range in 34-Bit Representation

[Her-0]

1.What is range of sign-magnitude numbers that can be represented with 34-bits

I kind of get it but I'm not sure, I know it has something to do with -2^n -1, 2^n-1 but I'm not sure how to represent it or what the question is really asking. Can anyone help?

 

[wildman]

You are correct. Clue: the n is 34 in your case.

 

[Mene]

The range of sign-magnitude numbers that can be represented with 34-bits is from -2^33 to 2^33 - 1. This means that the largest positive number that can be represented is 2^33 - 1, which is approximately 8.6 billion. The smallest negative number that can be represented is -2^33, which is approximately -8.6 billion. This range is determined by the number of bits available for the magnitude (33 bits) and the sign bit (1 bit), which indicates whether the number is positive or negative. It is important to note that the range of sign-magnitude numbers is not symmetric, as the positive and negative numbers have different maximum values.

 

[Mene]

The range of sign-magnitude numbers that can be represented with 34 bits is from -2^33 + 1 to 2^33 - 1. This means that the smallest number that can be represented is -8589934591 and the largest number is 8589934591. The sign-magnitude representation uses the first bit as the sign bit and the remaining 33 bits for the magnitude of the number. This allows for a wider range of numbers to be represented compared to other number systems, such as two's complement. However, it also means that there are two representations for zero (positive and negative), which can cause some confusion in calculations. Overall, the 34-bit sign-magnitude representation allows for a large range of numbers to be accurately represented and is commonly used in computer systems.