Please show your work What is the smallest number that can

Please show your work! :)

What is the smallest number that can be represented, and the largest number that can be represented in 1 Obits assuming that the bits are encoded as: unsigned sign and magnitude 1\'scomplement 2\'s complement

Solution

Answer:

10 bits for an unsigned number means it allows only positive integers. so using 10 bits, the number can range from 0 to 2^10 - 1. that is from 0 to 1023. (total 1024 numbers)

In sign magnitude representation, the most significant bit (leftmost bit) is used for representing the sign. if the leftmost bit is 1, the remaining 9 bits represent a negative number and when it is 0 it represents a positive integer. so here the range is -(2^9 - 1) to +(2^9 - 1), ie -511 to 511.

Same for 1s complement. 1s complement is just negating all bits of normal binary number (if its 0 it becomes 1 an vice-versa)