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, 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: