## Exercises2.6Exercises

###### 1.

Convert $$123_{10}$$ to binary.

Hint

123 % 2 = 1 so $$d_{0} = 1\text{.}$$ Then since 123 / 2 = 61, the next computation is 61 % 2 = 1.

$$\binary{1111011} = \hex{7b}$$

###### 2.

Convert the following unsigned decimal integers to 8-bit hexadecimal representation:

1. $$\displaystyle 100$$

2. $$\displaystyle 125$$

3. $$\displaystyle 10$$

4. $$\displaystyle 88$$

5. $$\displaystyle 255$$

6. $$\displaystyle 16$$

7. $$\displaystyle 32$$

8. $$\displaystyle 128$$

1. $$\displaystyle \hex{64}$$

2. $$\displaystyle \hex{7d}$$

3. $$\displaystyle \hex{0a}$$

4. $$\displaystyle \hex{58}$$

5. $$\displaystyle \hex{ff}$$

6. $$\displaystyle \hex{10}$$

7. $$\displaystyle \hex{20}$$

8. $$\displaystyle \hex{80}$$

###### 3.

Convert the following unsigned decimal integers to 16-bit hexadecimal representation:

1. $$\displaystyle 1024$$

2. $$\displaystyle 1000$$

3. $$\displaystyle 32768$$

4. $$\displaystyle 32767$$

5. $$\displaystyle 256$$

6. $$\displaystyle 65535$$

7. $$\displaystyle 4660$$

8. $$\displaystyle 43981$$

1. $$\displaystyle \hex{0400}$$

2. $$\displaystyle \hex{03e8}$$

3. $$\displaystyle \hex{8000}$$

4. $$\displaystyle \hex{7fff}$$

5. $$\displaystyle \hex{0100}$$

6. $$\displaystyle \hex{ffff}$$

7. $$\displaystyle \hex{1234}$$

8. $$\displaystyle \hex{abcd}$$

###### 4.

Invent a code that would allow us to store letter grades with plus or minus. That is, the grades A, A-, B+, B, B-,…, D, D-, F. How many bits are required for your code?

 Grade Code (in hex) A $$\binary{0000}$$ $$\hex{0}$$ A- $$\binary{0001}$$ $$\hex{1}$$ B+ $$\binary{0010}$$ $$\hex{2}$$ B $$\binary{0011}$$ $$\hex{3}$$ B- $$\binary{0100}$$ $$\hex{4}$$ C+ $$\binary{0101}$$ $$\hex{5}$$ C $$\binary{0110}$$ $$\hex{6}$$ C- $$\binary{0111}$$ $$\hex{7}$$ D+ $$\binary{1000}$$ $$\hex{8}$$ D $$\binary{1001}$$ $$\hex{9}$$ D- $$\binary{1010}$$ $$\hex{a}$$ F $$\binary{1011}$$ $$\hex{b}$$