What is the largest integer that can be represented with 8 bits? How many bits do you need to represent the largest integer + 1? How do you represent the numbers 8, -8, 200, and -200?

Exercises

For questions 1 – 3, answer each one for the case of a two’s complement number and an unsigned number, indicating if it cannot be answered with a specific representation.

1. (10 pts) What is the largest integer that can be represented with 8 bits? How many bits do you need to represent the largest integer + 1?

2. (8 pts) How do you represent the numbers 8, -8, 200, and -200 (assume the numbers are 8 bits)?

3. (4 pts) Is it possible to use 8 bits to represent the number 277? Is it possible to use 8 bits to represent the number -277? Explain why.

4. (10 pts) What is the range of decimals (presented with powers of 2) that 8-bit two’s complement can represent? What is the range of decimals that 12-bit two’s complement can represent?  Explain why.

5. (5 pts) How much data can we store on a 4 K-Byte memory chip?