Binary, Octal, Decimal, and Hexadecimal Number System Conversions Quiz Quiz

Sharpen your understanding of binary, octal, decimal, and hexadecimal conversions with this interactive quiz. Challenge your skills by identifying, comparing, and converting numbers across different base systems in a variety of practical scenarios.

1. Convert Binary to Decimal

   What is the decimal equivalent of the binary number 1010?

   1. 3
   2. 10
   3. 8
   4. 12

   Explanation: The binary number 1010 is calculated as 1×8 + 0×4 + 1×2 + 0×1, which equals 10 in decimal. Option 12 is incorrect, as that would result from 1100 in binary. The number 8 corresponds to binary 1000, while 3 is binary 0011. Only 10 correctly represents 1010 in decimal.

2. Understand Octal Numbers

   Which decimal number does the octal number 17 represent?

   1. 11
   2. 9
   3. 14
   4. 15

   Explanation: Octal 17 equals 1×8 + 7×1, which is 8+7=15. Option 14 represents octal 16. Option 11 in decimal is octal 13, and option 9 is octal 11. So 15 is the only correct decimal equivalent of octal 17.

3. Identify Hexadecimal to Binary

   What is the binary representation of the hexadecimal number C?

   1. 1010
   2. 1100
   3. 1111
   4. 1001

   Explanation: Hexadecimal C equals decimal 12, which is 1100 in binary. Option 1001 is binary for 9, 1010 is for decimal 10, and 1111 is for 15. Therefore, only 1100 translates to hexadecimal C in binary form.

4. Find Decimal from Hexadecimal

   What is the decimal equivalent of the hexadecimal number 1A?

   1. 21
   2. 30
   3. 26
   4. 16

   Explanation: Hexadecimal 1A equals 1×16 + 10×1 = 16 + 10 = 26. Option 21 corresponds to hexadecimal 15, 16 corresponds to hexadecimal 10, and 30 is not the result for 1A. Only 26 matches the correct conversion.

5. Choose the Octal for a Decimal

   Which is the correct octal representation of the decimal number 20?

   1. 25
   2. 24
   3. 20
   4. 16

   Explanation: To convert decimal 20 to octal, divide 20 by 8: 8×2=16, remainder 4, giving octal 24. Option 20 in octal is decimal 16. Option 16 is decimal 14 in octal, and 25 is decimal 21. So the correct octal representation is 24.

6. Binary to Octal Conversion

   What is the octal equivalent of the binary number 101100?

   1. 60
   2. 44
   3. 54
   4. 50

   Explanation: Grouping 101100 as 10 1100 makes two groups: 10 (2) and 1100 (12). Since octal digits go up to 7, we need to group as 010 (2) and 1100 (12). But for binary, it's grouped as 010 (2) and 110 (6), making 2 and 6 or octal 54. The other options do not match the grouping and value of the binary number.

7. Identifying a Hexadecimal Value

   Which of the following is a valid hexadecimal representation of the decimal number 31?

   1. 31
   2. 21
   3. 2F
   4. 1F

   Explanation: Hexadecimal 1F is 1×16 + 15×1 = 16+15=31. Option 31 is the decimal form. Option 21 in hexadecimal is 33 in decimal, and 2F is 47 in decimal. Only 1F is the correct hexadecimal equivalent for decimal 31.

8. Decimal to Binary Conversion

   What is the binary equivalent of the decimal number 13?

   1. 1101
   2. 1110
   3. 1001
   4. 1011

   Explanation: Decimal 13 in binary is 1101 (8+4+0+1). Option 1011 is 11, 1001 is 9, and 1110 is 14. Only 1101 matches the correct binary representation for 13.

9. Octal Reading in a Context Scenario

   If a device displays a status code of 77 in octal, what is its decimal value?

   1. 49
   2. 63
   3. 56
   4. 70

   Explanation: Octal 77 is 7×8 + 7×1 = 56+7=63. Option 49 corresponds to octal 61, 70 is octal 112, and 56 is octal 70. Therefore, 63 is the correct decimal value for octal 77.

10. Hexadecimal to Decimal with Double Digits

    What is the decimal value of the hexadecimal number 2A?

    1. 24
    2. 52
    3. 32
    4. 42

    Explanation: 2A in hexadecimal is 2×16 + 10 = 32 + 10 = 42. Option 24 is much smaller than the value, 32 is 20 in hexadecimal, and 52 is 34 in hexadecimal. So 42 is the correct decimal equivalent for 2A.