Enumerate all of the unique values that a two-bit binary number can have. (2 pts) ...

Enumerate all of the unique values that a two-bit binary number can have. (2 pts)

How many total unique values are there? (2 pts)

Based on the value of the left-most bit, divide the above binary numbers into two groups, such that within each group, all of the numbers have the same left-most bit. (2 pts)

Remove the left-most bit from the numbers in each group. (2 pts)

Are the two groups now identical? (2 pts)

How many total unique values are there now? (2 pts)

By what ratio has the total number of unique values changed? (2 pts)

Start again by enumerating all of the unique values that a two-bit binary number can have. But this time, write out the set of values twice, in two separate groups. (2 pts)

How many total unique values are there? (2 pts)

Add an extra bit to the left of all of the numbers - add a 0 to the set in one of the groups and add a 1 to the set in the other group. (2 pts)

How many total unique values are there now? (2 pts)

By what ratio has the total number of unique values changed? (2 pts)

How many unique values can be expressed with a 1 digit binary number (express your answer in both exponential and non-exponential base 10) (2 pts)? What are the lowest and highest values (in base 10) (1 pt)?

How many unique values can be expressed with a 2 digit binary number (express your answer in both exponential and non-exponential base 10) (2 pts)? What are the lowest and highest values (in base 10) (1 pt)?

How many unique values can be expressed with a 3 digit binary number (express your answer in both exponential and non-exponential base 10) (2 pts)? What are the lowest and highest values (in base 10) (1 pt)?

How many unique values can be expressed with a 4 digit binary number (express your answer in both exponential and non-exponential base 10) (2 pts)? What are the lowest and highest values (in base 10) (1 pt)?

How many unique values can be expressed with a 5 digit binary number (express your answer in both exponential and non-exponential base 10) (2 pts)? What are the lowest and highest values (in base 10) (1 pt)?

How many unique values can be expressed with a 6 digit binary number (express your answer in both exponential and non-exponential base 10) (2 pts)? What are the lowest and highest values (in base 10) (1 pt)?

How many unique values can be expressed with a 7 digit binary number (express your answer in both exponential and non-exponential base 10) (2 pts)? What are the lowest and highest values (in base 10) (1 pt)?

How many unique values can be expressed with a 8 digit binary number (express your answer in both exponential and non-exponential base 10) (2 pts)? What are the lowest and highest values (in base 10) (1 pt)?