## Exercises2.2Exercises

###### 1.

Express the following bit patterns in hexadecimal.

1. $$\displaystyle \binary{0100} \; \binary{0101} \; \binary{0110} \; \binary{0111}$$

2. $$\displaystyle \binary{1000} \; \binary{1001} \; \binary{1010} \; \binary{1011}$$

3. $$\displaystyle \binary{1111} \; \binary{1110} \; \binary{1101} \; \binary{1100}$$

4. $$\displaystyle \binary{0000} \; \binary{0010} \; \binary{0101} \; \binary{0010}$$

1. $$\displaystyle \hex{4567}$$

2. $$\displaystyle \hex{89ab}$$

3. $$\displaystyle \hex{fedc}$$

4. $$\displaystyle \hex{0252}$$

###### 2.

Express the following bit patterns in binary.

1. $$\displaystyle \hex{83af}$$

2. $$\displaystyle \hex{9001}$$

3. $$\displaystyle \hex{aaaa}$$

4. $$\displaystyle \hex{5555}$$

1. $$\displaystyle \binary{1000} \; \binary{0011} \; \binary{1010} \; \binary{1111}$$

2. $$\displaystyle \binary{1001} \; \binary{0000} \; \binary{0000} \; \binary{0001}$$

3. $$\displaystyle \binary{1010} \; \binary{1010} \; \binary{1010} \; \binary{1010}$$

4. $$\displaystyle \binary{0101} \; \binary{0101} \; \binary{0101} \; \binary{0101}$$

###### 3.

How many bits are represented by each of the following?

1. $$\displaystyle \hex{ffff} \; \hex{ffff}$$

2. $$\displaystyle \hex{7fff} \; \hex{58b7} \; \hex{def0}$$

3. $$\displaystyle \binary{1111}_{2}$$

4. $$\displaystyle \hex{1111}_{16}$$

Hint

Don't forget that each hexadecimal digit represents 4 bits.

1. $$\displaystyle 32$$

2. $$\displaystyle 48$$

3. $$\displaystyle 4$$

4. $$\displaystyle 16$$

###### 4.

How many hexadecimal digits are required to represent each of the following?

1. eight bits

2. thirty-two bits

3. sixty-four bits

4. ten bits

5. twenty bits

6. seven bits

Hint

One hexadecimal digit is required to represent one–four bits.

1. $$\displaystyle 2$$
2. $$\displaystyle 8$$
3. $$\displaystyle 16$$
4. $$\displaystyle 3$$
5. $$\displaystyle 5$$
6. $$\displaystyle 2$$