Chapter 2 Number System

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A Name the following.

  1. Rightmost digit of a number. Least Significant Digit (LSD)
  2. Leftmost digit of a number. Most Significant Digit (MSD)
  3. Digits of binary number system. Bits
  4. Two examples of hexadecimal number system: FACE, 3D5
  5. Base of hexadecimal number system. 16

B State whether the following statements are true or false.

  1. The positional value of each digit increases from right to left. True
  2. The base of binary number system is 8. False
  3. Decimal number system has a base as 0. False
  4. The instructions given to a computer is converted into decimal language. False
  5. The base of octal number system is 8. True

C Fill in the blanks.

  1. To convert binary number system to decimal number system, we multiply each digit with its positional value.
  2. The octal system consists of 8 digits.
  3. Binary addition is similar to decimal addition.
  4. Any quantity greater than 9 is represented by a contribution of two or more digits.
  5. The number system consists of a set of values.

D Convert the following.

  1. (24)10 = (?)2 = 1 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 0 × 20 = (11000)2
  2. (4D2)16 = (?)10 = 4 × 162 + 13 × 161 + 2 × 160 = 1024 + 208 + 2 = (1234)10
  3. (64A)16 = (?)10 = 6 × 162 + 4 × 161 + 10 × 160 = 1536 + 64 + 10 = (1610)10
  4. (344)8 = (?)10 = 3 × 82 + 4 × 81 + 4 × 80 = 192 + 32 + 4 = (228)10
  5. (10)10 = (?)2 = 1 × 23 + 0 × 22 + 1 × 21 + 0 × 20 = (1010)2

E Answer the following questions.

  1. Write the rules to perform the following conversions.
    (a) Hexadecimal number system to decimal number system.
    Multiply each digit with its positional value, keeping base as 16.
    (b) Octal number system to decimal number system.
    Multiply each digit with its positional value, keeping base as 8.
    (c) Binary number system to decimal number system.
    Multiply each digit with its positional value, keeping base as 2.
    (d) Decimal to binary number system.
    Keep dividing the number by 2 until the quotient becomes 0. During each division, note the remainders. Finally, arrange the remainders, going from last remainder to the first remainder.
  2. Add 101 with 101.
    Answer: 1010
  3. Subtract 11 from 101.
    Answer: 10
  4. Multiply 111 with 001.
    Answer: 111
  5. Divide 1101 with 111.
    Quotient: 1
    Remainder: 110

Extra Questions.

  1. A number system consists of a set of digits.
  2. Decimal number system is the most commonly used number system.
  3. The octal number system consists of 8 digits.
  4. The decimal number system consists of 10 digits.
  5. The hexadecimal number system consists of 16 digits.
  6. The binary number system consists of 2 digits.
  7. Binary addition is similar to addition of decimal numbers.
  8. The base of the hexadecimal number system is 16.
  9. The base of the decimal number system is 10.
  10. The base of the octal number system is 8.
  11. The base of the binary number system is 2.
  12. The instructions given to a computer are converted into binary language.
  13. The rightmost digit of a number is called LSD.
  14. The leftmost digit of a number is called MSD.
  15. Gottfried Leibniz invented the modern binary number system.
  16. The positional value of each digit increases as we move from left to right. (True/False)
  17. Binary subtraction is very similar to subtraction of decimal numbers. (True/False)
  18. Binary multiplication is very similar to multiplication of decimal numbers. (True/False)
  19. Binary addition generates a carryover when the sum of two binary digits exceeds 1. (True/False)
  20. In binary subtraction, a borrow is taken from the next higher bit when subtracting a higher bit from a lower bit. (True/False)
  21. Binary multiplication results in 1 only when both multiplicands are 1. (True/False)
  22. Which number system do we use?
    Decimal Number System
  23. List the digits supported in the binary number system.
    0 and 1
  24. List the digits supported in the octal number system.
    0, 1, 2, 3, 4, 5, 6, 7
  25. List the digits supported in the hexadecimal number system.
    0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
  26. List the digits supported in the decimal number system.
    0, 1, 2, 3, 4, 5, 6, 7, 8, 9
  27. Convert 2810 to binary number system.
    111002
  28. Convert 101102 to decimal number system.
    2210
  29. Convert 2538 into decimal number system.
    17110
  30. Convert FD216 into decimal number system.
    405010
  31. Add 11012 with 10112.
    110002
  32. Subtract 1102 from 110012.
    100112
  33. Multiply 111102 with 1012.
    110101102
  34. Divide 1011012 with 1102 and find the quotient and the remainder.
    Quotient = 1112
    Remainder = 112

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