Numbering Systems Problems

Question 1

State the main characteristics and uses of the following numbering systems.
  1. Binary
  2. Octal
  3. Decimal (or Denary)
  4. Hexadecimal

Question 2

State the number of bits in the following sizes of binary number.
  1. bit
  2. nibble
  3. byte

Question 3

Convert the following binary numbers to decimal form.
  1. 10012
  2. 11 01002
  3. 0110 10112
  4. 1001 1110 01012
  5. 0010 1111 1010 01012

Question 4

Convert the following decimal numbers to binary form.
  1. 1110
  2. 4210
  3. 170 10
  4. 2,92010
  5. 21,78010

Question 5

Convert the following binary numbers to octal form.
  1. 01102
  2. 10 10012
  3. 0111 10112
  4. 1100 1000 10112
  5. 011 1001 0100 00102

Question 6

Convert the following octal numbers to binary form.
  1. 58
  2. 758
  3. 3568
  4. 57168
  5. 714368

Question 7

Convert the following hexadecimal numbers to binary form.
  1. C16
  2. 4A16
  3. 78F16
  4. 357916
  5. ABCD16

Question 8

Convert the following binary numbers to hexadecimal form.
  1. 10102
  2. 10 11002
  3. 1111 11012
  4. 101 1011 10002
  5. 111 1010 0100 00112

Question 9

Convert the following decimal numbers to hexadecimal form.
  1. 910
  2. 3410
  3. 45610
  4. 2,98110
  5. 38,71610

Question 10

Convert the following hexadecimal numbers to decimal form.
  1. E16
  2. 2A16
  3. 14C16
  4. 3AE716
  5. FFFF16
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Question 1

  1. Binary (base 2) is the numbering system used internally by digital computers. Each digit in a binary number is either 0 or 1 and moving to the left, the place value of each digit doubles (1, 2, 4, 8 etc.).
  2. Octal (base 8) is normally used as a shorthand representation of binary numbers, since each octal value is equivalent to 3 binary digits. Each octal digit can vary in the range 0-7 and, moving to the left, the place value of each digit increases by a factor of eight.
  3. Decimal (or denary) is the base 10 numbering system with which we are most familiar. Each decimal digit can vary in the range 0–9 and moving to the left, the value of a digit increases by a factor of 10. Octal or hexadecimal are more commonly used as shorthand representations of binary values due to the difficulty of conversion between decimal and binary.
  4. Hexadecimal (base 16) is normally used to represent binary numbers in a more compact form, with each hexadecimal value equivalent to 4 binary digits. Each hexadecimal digit may vary in the range 0–15, the digits being represented by numeric characters O–9 and letters A–F. Moving to the left each digit is worth 16 times as much as the digit immediately to the right.

Question 2

  1. 1
  2. 4
  3. 8

Question 3

  1. 910
  2. 5210
  3. 10710
  4. 2,53310
  5. 12,19710

Question 4

  1. 10112
  2. 10 10102
  3. 1010 10102
  4. 1011 0110 10002
  5. 101 0101 0001 01002

Question 5

  1. 68
  2. 518
  3. 1738
  4. 62138
  5. 345028

Question 6

  1. 1012
  2. 11 11012
  3. 1110 11102
  4. 1011 1100 11102
  5. 111 0011 0001 11102

Question 7

  1. 11002
  2. 100 10102
  3. 111 1000 11112
  4. 11 0101 0111 10012
  5. 1010 1011 1100 11012

Question 8

  1. A16
  2. 2C16
  3. FD16
  4. 5B816
  5. 7A4316

Question 9

  1. 916
  2. 2216
  3. 1C816
  4. BA516
  5. 973C16

Question 10

  1. 1410
  2. 4210
  3. 33210
  4. 15,07910
  5. 65,53510

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