Homework 2 -- Computer Representation of Integers

Convert the following numbers from the bases as indicated.

a.      306  (octal)              ______________________  (binary) 

b.      2E5  (hex)                ______________________  (binary)

c.      11101010 (binary)         ______________________  (octal) 

d.      11101010 (binary)        ______________________  (hex) 

e.      306   (octal)              ______________________  (hex) 

f.      2E5   (hex)                ______________________  (octal)

What is the biggest numeric value you can write in 10 bits using two's complement notation? Express it in both binary two's complement form and in decimal:
```
two's comp  __________________________  decimal  ________________________
```
What is the smallest numeric value you can write in 10 bits using two's complement notation? Express it in both binary two's complement form and in decimal:
```
two's comp  __________________________  decimal  ________________________
```

Convert the following decimal values to binary two's complement notation in 8 bits:

a.   -81           ______________________

b.    -2           ______________________

c.    88           ______________________

d.   -45           ______________________

e.     1           ______________________

f.  -122           ______________________

Is it possible to express +1024 in 11 bits using two's complement notation? If so, then write it below.
```
________________________
```
Is it possible to express +1024 in 11 bits if we use unsigned numbers? If so, then write it below.
```
________________________
```
What is the biggest value we can express in 32 bits if we use unsigned numbers? Express it in both binary and in decimal:
```
binary  __________________________  decimal  ________________________
```
What is the smallest value we can express in 32 bits if we use unsigned numbers? Express it in both binary and in decimal:
```
binary  __________________________  decimal  ________________________
```

What are the decimal values of the following numbers, given that they are written using 8-bit two's complement notation?

a.	11010110		______________________

b.	10110010		______________________

c.	00011001		______________________

d.	01000101		______________________

e.	11110111		______________________

Suppose we use a machine that represents integers in 9 bits using two's complement notation.

a.	Our integers act like what set of modulo numbers?  _________________

b.	How many integers can be represented in the machine? _______________

c.	What is the largest possible positive integer?  Express it in both binary and decimal.

	binary:  _______________________  decimal:  ______________________

d.	What is the smallest possible negative integer?  Express it in both binary and decimal.

	binary:  _______________________  decimal:  ______________________

What is the smallest number of bits that can be used to store an integer on a computer which must be able to handle integers ranging from 2,000,000,000 down to -2,000,000,000?
```
_______________________
```
What if the computer represents integers in a fixed number of bytes? What is the fewest number of bytes necessary to handle integers ranging from 2,000,000,000 down to -2,000,000,000?
```
_______________________
```