Q 1.1 - Binary, Octal, Hexadecimal Questions

1. Count from 24 to 34 in decimal, binary, octal and hexadecimal.

2. Count from 56 to 66 in decimal, binary, octal and hexadecimal.

3. Count from 81 to 91 in decimal, binary, octal and hexadecimal.

4. Convert these decimal numbers in to binary, octal and hexadecimal.

  1. 123

  2. 12

  3. 26

  4. 36

  5. 99

  6. 100

  7. 82

 5. Convert these numbers from binary to decimal.

  1. 1010

  2. 1100

  3. 1001

  4. 101010

  5. 110001

  6. 111111

  7. 1011010

  8. 1101001

  9. 1110100

 6. Convert these numbers from octal to decimal.

  1. 723

  2. 127

  3. 342

  4. 65421

  5. 23127

  6. 23872

 7. Convert these numbers from hexadecimal to decimal.

  1. a3

  2. 4e

  3. 5f

  4. af2

  5. e4d

  6. 32a

 8. Convert these binary numbers to octal.

  1. 101011

  2. 100110

  3. 111111

  4. 111010

  5. 110001

  6. 101110

 9. Convert these binary numbers to hexadecimal

  1. 1001

  2. 1011

  3. 1010

  4. 1111

  5. 0011

  6. 0101

  7. 11010010

  8. 11001001

  9. 10010110

  10. 10101010

  11. 10110011

  12. 10100110

 10. Convert these decimal numbers in to binary, octal and hexadecimal.

  1. 8.75

  2. 10.5

  3. 3.3125

  4. 5.75

  5. 9.25

  6. 6.6875

  7. 2.8125

  8. 11.4375

 11. What possible bases could each number have? (Look at the largest digit) Assume letters work as in hexadecimal.

  1. 1011

  2. 123

  3. 237

  4. 983

  5. 2b

  6. a2g

  7. 5zw

 12. Suppose a number has a base 8.

  1. What digits could be used in the number?

  2. What would the first four columns be?

 13. Suppose a number has a base 4.

  1. What digits could be used in the number?

  2. What would the first four columns be?

  3. What is decimal 12 in written in this base system?

 14. Which of the following would make a good base for a number system? Justify your choices.

  1. 5

  2. 23

  3. 23456

  4. 0.4

  5. p

  6. ½

  7. 0

  8. 1

  9. -1

  10. -23

 15. (a) Why are binary, octal and hexadecimal the number systems used most often by computer scientists?
(b) Why is it easy to convert numbers between binary, octal and hexadecimal? What other bases would it be easy to translate between?