## Exercises2.4Exercises

###### 1.

Referring to Equation (2.3.3), what are the values of $$r\text{,}$$ $$n$$ and each $$d_{i}$$ for the decimal number $$29458254\text{?}$$ The hexadecimal number $$\hex{29458254}\text{?}$$

Decimal number: $$r = 10, n = 8, d_{7} = 2, d_{6} = 9, d_{5} = 4, d_{4} = 5, d_{3} = 8, d_{2} = 2, d_{1} = 5, d_{0} = 4$$

Hexadecimal number: $$r = 16, n = 8, d_{7} = 2, d_{6} = 9, d_{5} = 4, d_{4} = 5, d_{3} = 8, d_{2} = 2, d_{1} = 5, d_{0} = 4$$

###### 2.

Convert the eight-digit binary number $$\binary{1010} \; \binary{0101}$$ to decimal.

\begin{align*} \binary{1010} \; \binary{0101}_{2} &= 1 \times 2^{7} + 0 \times 2^{6} + 1 \times 2^{5} + 0 \times 2^{4} + 0 \times 2^{3} + 1 \times 2^{2} + 0 \times 2^{1} + 1 \times 2^{0}\\ &= 128 + 0 + 32 + 0 + 0 + 4 + 0 + 1 \\ &= 165_{10} \end{align*}
###### 3.

Convert the following 8-bit binary numbers to decimal by hand:

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

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

3. $$\displaystyle \binary{1111} \; \binary{0000}$$

4. $$\displaystyle \binary{0000} \; \binary{1111}$$

5. $$\displaystyle \binary{1000} \; \binary{0000}$$

6. $$\displaystyle \binary{0110} \; \binary{0011}$$

7. $$\displaystyle \binary{0111} \; \binary{1011}$$

8. $$\displaystyle \binary{1111} \; \binary{1111}$$

1. $$\displaystyle 170$$

2. $$\displaystyle 85$$

3. $$\displaystyle 240$$

4. $$\displaystyle 15$$

5. $$\displaystyle 128$$

6. $$\displaystyle 99$$

7. $$\displaystyle 123$$

8. $$\displaystyle 255$$

###### 4.

Convert the following 16-bit binary numbers to decimal by hand:

1. $$\displaystyle \binary{1010} \; \binary{1011} \; \binary{1100} \; \binary{1101}$$

2. $$\displaystyle \binary{0001} \; \binary{0010} \; \binary{0011} \; \binary{0100}$$

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

4. $$\displaystyle \binary{0000} \; \binary{0111} \; \binary{1101} \; \binary{1111}$$

5. $$\displaystyle \binary{1000} \; \binary{0000} \; \binary{0000} \; \binary{0000}$$

6. $$\displaystyle \binary{0000} \; \binary{0100} \; \binary{0000} \; \binary{0000}$$

7. $$\displaystyle \binary{0111} \; \binary{1011} \; \binary{1010} \; \binary{1010}$$

8. $$\displaystyle \binary{0011} \; \binary{0000} \; \binary{0011} \; \binary{1001}$$

1. $$\displaystyle 43981$$

2. $$\displaystyle 4660$$

3. $$\displaystyle 65244$$

4. $$\displaystyle 2015$$

5. $$\displaystyle 32768$$

6. $$\displaystyle 1024$$

7. $$\displaystyle 31658$$

8. $$\displaystyle 12345$$

###### 5.

Develop an algorithm to convert hexadecimal to decimal, and then convert the following 16-bit numbers to decimal by hand:

1. $$\displaystyle \hex{a000}$$

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

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

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

5. $$\displaystyle \hex{8888}$$

6. $$\displaystyle \hex{0190}$$

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

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

Hint

Review the algorithm to convert binary to decimal above.

1. Set $$Result = 0$$

2. For $$i = 0, \cdots, (n-1)$$

• $$\displaystyle Result = Result + d_{i} * 16^{i}$$

1. $$\displaystyle 40960$$

2. $$\displaystyle 65535$$

3. $$\displaystyle 1024$$

4. $$\displaystyle 4369$$

5. $$\displaystyle 34952$$

6. $$\displaystyle 400$$

7. $$\displaystyle 43981$$

8. $$\displaystyle 21845$$