Explore foundational concepts in modular arithmetic and number systems with this beginner-friendly quiz. Sharpen your problem-solving skills across remainders, congruence, binary, hexadecimal, and applications of arithmetic modulo operations.
What is the remainder when 17 is divided by 5?
Explanation: When you divide 17 by 5, 5 goes into 17 three times (5 x 3 = 15) with a remainder of 2. Option '3' is the quotient, not the remainder. Option '1' could be confused with the difference between 17 and the next multiple of 5 (20 - 17). Option '5' would indicate no remainder, which is not true here.
Which of the following correctly expresses that 23 and 8 have the same remainder when divided by 5?
Explanation: The notation '23 ≡ 8 (mod 5)' means 23 and 8 have the same remainder modulo 5, which is correct. '23 ≠ 8 (mod 5)' is the opposite statement. '23 ≡ 8 (mod 8)' refers to modulo 8, which is unrelated to this question. '23 = 8 (mod 5)' uses an incorrect symbol for modular congruence.
Which of these numbers represents the decimal number 5 in binary?
Explanation: The decimal number 5 is represented as '101' in binary (1×4 + 0×2 + 1×1 = 5). '110' corresponds to 6, '100' to 4, and '111' to 7. Choosing these distractors helps illustrate how each bit value affects the overall decimal value.
What is the result of (4 + 9) mod 7?
Explanation: Adding 4 and 9 gives 13, and 13 divided by 7 leaves a remainder of 6. '0' would be the case if 13 were a multiple of 7. '5' comes from subtracting 7 just once (13 - 7 = 6), possibly confusing those not looking for the remainder. '1' is incorrect, as 13 mod 7 does not give 1.
What is the decimal value of the hexadecimal number 'A'?
Explanation: In hexadecimal, 'A' represents the decimal value 10. '11' and '12' are the values for 'B' and 'C' respectively. '9' is just before 'A' in hexadecimal, with the letter sequence starting at 10.
Is 36 divisible by 4 as determined by modular arithmetic?
Explanation: A number is divisible by another if its modulus with that number is 0. 36 divided by 4 equals 9 with a remainder of 0. Options with remainders 1, 2, or 3 are incorrect, as any non-zero remainder indicates indivisibility.
What is the decimal equivalent of the binary number 1101?
Explanation: Converting 1101 from binary: (1 × 8) + (1 × 4) + (0 × 2) + (1 × 1) = 8 + 4 + 1 = 13. '11' and '9' represent incorrect summations, missing the full place values. '15' would be 1111 in binary.
Calculate (7 × 5) mod 6.
Explanation: 7 times 5 is 35, and 35 divided by 6 leaves a remainder of 5. '1' is incorrect and may be a confusion with 7 mod 6. '0' would be correct if 35 were a multiple of 6. '4' is unrelated to the calculation.
Which number system uses base 8 and digits from 0 to 7?
Explanation: The octal number system uses base 8, so its digits range from 0 to 7. Decimal is base 10, hexadecimal is base 16, and binary is base 2. Choosing decimal, hexadecimal, or binary confuses bases and digit ranges.
Which scenario best demonstrates modular arithmetic in everyday life?
Explanation: Days of the week cycle in a repeating pattern, so modular arithmetic helps determine the correct day after a certain interval. Adding fractions typically does not involve modular operations. Solving algebraic equations and measuring temperatures are not directly associated with modular arithmetic.