**Question 1 (10 pts),** Using **weights** in base 8, convert 1012_{(10) }into base 8, convert 2031_{(10) }into base 8.

**Question 2 (10 pts),** Use the **division** conversion method to convert decimal number2031_{(10) }into base 8. Compare your answer with the above question 1.

**Question 3 (10 pts),** Use the **division** method to convert a decimal number3095_{(10) }to base 16. Verify your answer by using the weights method to convert your answer back to base 10.

**Question 4 (10 pts),** Use the **multiplication** method to convert 11000110_{(2) }to base 10. Verify your answer by using the weights method to convert the number back to base 2.

**Question 5 (12 pts),** Convert the number 11010011 1011_{(2) }directly from binary to hexadecimal. Write a mapping list of binary (from 0000 to 1111) to hex numbers.

**Question 6 (6+6+6+6 pts), **

a.) Use the following decimal addition/multiplication tables as example, create the **hexadecimal **addition/ multiplication tables.

** **

** **

**Use your hexadecimal tables to perform the following addition and multiplication, make sure to write detailed HEX multiplication steps: **

- 3E5A + 467D
- 23AB + 509
- 4F35 x 2B

**Question 7 (12 pts), **

Just like decimal multiplication, binary multiplication could also be converted as adding a series of numbers. For example, 2_{10}x3_{10} = 2_{10}+2_{10}+2_{10} in decimal number system, similarly, in binary number system 10_{2} x 11_{2} = 10_{2} (shift left by 1 bit) + 10_{2}, meaning 10_{2} times 2 then adds with 10_{2} again. Using this method, solve the following **binary multiplication**, make sure to write detailed BINARY calculation steps:

a.) 1010_{2} × 110_{2}

b.) 10110_{2} × 1001_{2}

**Question 8 (12 pts) **

Now please perform the binary division. Still remember how to do decimal division? 5_{10}/2_{10} is calculated by 5_{10}– 2_{10} x 2 = 1 making the quotient 2 and remainder 1. Binary division is similar, but simpler – since the quotient in each division step can only be either 1 or 0 (1 means dividend >= divisor, while 0 means dividend < divisor). Use this method to solve the following **binary division**, make sure to write detailed BINARY calculation steps:

a.) 1011011101_{2}/101_{2}

b.) 11001001010_{2}/1101_{2}

Last Updated on