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Knowledge Quiz

Test your understanding of number systems

Instructions

Answer all 15 questions to test your knowledge of binary, denary, and hexadecimal number systems. You'll see your results at the end.

Topics covered: Binary/denary conversion, hexadecimal conversion, binary addition, overflow errors, binary shifts, MSB/LSB

Question 1

What is the denary (decimal) value of the binary number 11001010?

Explanation: 11001010 = 128 + 64 + 0 + 0 + 8 + 0 + 2 + 0 = 202

Question 2

What is 173 in 8-bit binary?

Explanation: 173 = 128 + 32 + 8 + 4 + 1 = 10101101 in binary

Question 3

What is the hexadecimal equivalent of the binary number 11110101?

Explanation: Split into nibbles: 1111 = 15 = F, 0101 = 5. Answer: F5

Question 4

What is the denary value of hexadecimal B9?

Explanation: B = 11, 9 = 9. So B9 = (11 × 16) + (9 × 1) = 176 + 9 = 185

Question 5

What is the result of adding these two binary numbers: 01010011 + 00101101?

Explanation: 01010011 (83) + 00101101 (45) = 128 = 10000000

Question 6

When does an overflow error occur in 8-bit binary addition?

Explanation: An overflow error occurs when the result is too large to fit in the available bits. For 8-bit unsigned integers, this means any result greater than 255.

Question 7

What does MSB stand for?

Explanation: MSB = Most Significant Bit, which is the leftmost bit in a binary number and has the highest place value.

Question 8

What is the result of left-shifting 00011010 by 2 positions?

Explanation: Left shift by 2: 00011010 → 01101000. The original value (26) becomes 104 (26 × 4).

Question 9

What operation does a binary right shift by 1 perform?

Explanation: A right shift by 1 divides by 2 (using integer division, which rounds down).

Question 10

What is the maximum denary value that can be stored in 8 bits (unsigned)?

Explanation: 8 bits can represent 2^8 = 256 different values (0-255). The maximum is 11111111 = 255.

Question 11

Which hexadecimal digit represents the denary value 13?

Explanation: In hex: A=10, B=11, C=12, D=13, E=14, F=15. So D represents 13.

Question 12

What is the binary result of 1 + 1 + 1 in binary addition?

Explanation: 1 + 1 + 1 = 3 in denary, which is 11 in binary. So we write 1 and carry 1 to the next column.

Question 13

Convert the hexadecimal number FF to denary.

Explanation: F = 15, so FF = (15 × 16) + (15 × 1) = 240 + 15 = 255

Question 14

In the binary number 10110100, what is the place value of the LSB (Least Significant Bit)?

Explanation: The LSB (Least Significant Bit) is always the rightmost bit, which always has a place value of 1, regardless of what digit is in that position.

Question 15

What is 01010000 right-shifted by 3 positions?

Explanation: 01010000 (80 in denary) right-shifted by 3 = 00001010 (10 in denary). This is 80 ÷ 8 = 10.
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