Computer science homework

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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:

  1. 3E5A + 467D
  2. 23AB + 509
  3. 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, 210x310 = 210+210+210 in decimal number system, similarly, in binary number system 102 x 112 = 102 (shift left by 1 bit) + 102, meaning 102 times 2 then adds with 102 again. Using this method, solve the following binary multiplication, make sure to write detailed BINARY calculation steps:

 

a.) 10102 × 1102

 

b.) 101102 × 10012

 

Question 8 (12 pts)

Now please perform the binary division. Still remember how to do decimal division? 510/210 is calculated by 510–  210 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.) 10110111012/1012

 

b.) 110010010102/11012

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