Deepen your understanding of number systems with this quiz covering binary, decimal, octal, and hexadecimal essentials. Assess your skills in conversions, representations, and conceptual differences across these foundational digital systems.
What is the decimal value of the binary number 1101?
Explanation: The binary number 1101 equals 13 in decimal because 1*8 (2) + 1*4 (2²) + 0*2 (2¹) + 1*1 (2⁰) = 8 + 4 + 0 + 1 = 13. Option 11 corresponds to binary 1011, and 15 is binary 1111. Option 9 would correspond to binary 1001. Only 13 is correct for 1101.
Which hexadecimal value represents the decimal number 31?
Explanation: Decimal 31 is written as 1F in hexadecimal because 1*16 (16¹) + 15*1 (F=15 for 16⁰) = 16 + 15 = 31. Option 2E equals decimal 46, 23 equals decimal 35, and 1E is 30. Therefore, 1F is the only correct representation for 31.
What is the octal equivalent of the binary number 101110?
Explanation: To convert binary 101110 to octal, group as 010 (2) and 111 (7) and 0 (0), so it becomes 56 in octal (101=5, 110=6). Option 44 is binary 100100, 36 is binary 011110, and 62 is binary 110010. Only 56 accurately represents binary 101110 in octal.
In the decimal system, what is the value of the digit 7 in the number 2,471, given its position?
Explanation: In 2,471, the 7 is in the tens place, so its value is 7*10 = 70. 700 would be the case if it was in the hundreds place, and 7000 would be for the thousands place. Simply 7 does not take into account the place value, but 70 reflects its correct position in the number.
Which statement correctly describes the range of single-digit values in the hexadecimal number system?
Explanation: Hexadecimal single digits use 0 to F (0–9 and A–F for 10–15), covering all possible digit values in base-16. 0 to 8 omits both 9 and the letters A-F, while 1 to F incorrectly starts from 1 and misses 0. 0 to 9 is incomplete for hexadecimal, as it misses the letters used for 10–15.