Number Bases and Modular Arithmetic

You are signed in with your email. Delete my email

Pick an answer to check it. Answers and working are free for students who sign in with their email.

1. Convert the base-10 number 45 into base 6.

   1. A 311
   2. B 131
   3. C 113
   4. D 73

2. Calculate (23)_4 + (12)_4 in base 4.

   1. A 35
   2. B 111
   3. C 100
   4. D 101

3. Find the remainder when 2^10 is divided by 7.

   1. A 1
   2. B 2
   3. C 4
   4. D 6

4. Convert the base-5 number 23.41 to base 10.

   1. A 13.41
   2. B 13.84
   3. C 12.84
   4. D 14.84

5. Express the base-10 number 15.75 in base 2.

   1. A 1110.11
   2. B 1111.01
   3. C 1111.11
   4. D 1111.10

6. Find the value of 7 × 8 in modulo 9 arithmetic.

   1. A 5
   2. B 8
   3. C 1
   4. D 2

8. If x ≡ 3 (mod 7) and y ≡ 5 (mod 7), find the value of x + y in modulo 7 arithmetic.

   1. A 8
   2. B 0
   3. C 1
   4. D 2

9. Solve for x in the congruence 3x ≡ 10 (mod 11).

   1. A 4
   2. B 6
   3. C 7
   4. D 8

← All Mathematics topics Next topic: Fractions, Decimals, Approximations and Percentages →