Sample Quizzes For Preparation: Number Systems

O Level and IGCSE Computer Science – Chapter 1.1 Number Systems Quiz

Q1.

Which of the following number systems is used internally by computers to store data?
A) Denary
B) Binary
C) Octal
D) Hexadecimal

Q2.

What is the binary equivalent of the decimal number 13?
A) 1101
B) 1110
C) 1001
D) 1010

Q3.

What is the main advantage of using hexadecimal over binary for humans?
A) It is easier for calculations
B) It uses only two digits
C) It is more accurate
D) It is shorter and easier to read

Q4.

What is the decimal value of the binary number 10011010?
A) 156
B) 157
C) 154
D) 155

Q5.

Which hexadecimal number is equivalent to binary 11110000?
A) F0
B) 0F
C) A0
D) FF

Q6.

How many bits are grouped together to represent one hexadecimal digit?
A) 2
B) 4
C) 6
D) 8

Q7.

What happens in a left binary shift by 1 bit?
A) The value is halved
B) The value is doubled
C) A zero is added to the left
D) A one is added to the right

Q8.

What is the result of adding binary 10101010 and 01010101?
A) 11111111
B) 00000000
C) 10000000
D) 11011011

Q9.

What condition leads to overflow in binary addition?
A) Subtracting a larger number from a smaller one
B) When result fits in given bits
C) When result exceeds the max value storable in bits
D) When adding two zeros

Q10.

Which of the following is NOT a valid hexadecimal digit?
A) D
B) G
C) 9
D) B

Q11.

What is the hexadecimal equivalent of decimal number 255?
A) EE
B) 1A
C) FF
D) F1

Q12.

What is the 8-bit binary representation of hexadecimal 3C?
A) 00111100
B) 11110011
C) 00110011
D) 11111100

Q13.

What is the effect of a 2-bit right shift on binary number 00110000?
A) 00001100
B) 11000000
C) 00000011
D) 00000110

Q14.

What is the 8-bit two’s complement representation of -1?
A) 11111111
B) 10000000
C) 00000001
D) 00000000

Q15.

What is the result when -18 is converted to 8-bit two’s complement binary?
A) 11101101
B) 11101110
C) 11100010
D) 11110010

Q16.

Which of the following ranges correctly defines the two’s complement range for 8-bit values?
A) -127 to +128
B) -256 to +255
C) -128 to +127
D) -128 to +128

Q17.

What happens to the most significant bit (MSB) in two’s complement for negative numbers?
A) It is always 0
B) It is ignored
C) It is always 1
D) It is used for parity

Q18.

Which operation is used in the second step when converting a negative number to two’s complement?
A) Multiplying by -1
B) Subtracting from 255
C) Inverting bits
D) Adding 1

Q19.

Which number system uses base 16?
A) Decimal
B) Octal
C) Binary
D) Hexadecimal

Q20.

What is the hexadecimal representation of binary number 11010111?
A) D7
B) 1F
C) F1
D) E4

Answer Key with Explanations – O Level and IGCSE Computer Science – Chapter 1.1 Number Systems

Q1. B) Binary

• Correct: Computers use binary (0s and 1s) because their circuits only recognize two states.
• Incorrect: Denary, octal, and hexadecimal are for human use, not internal machine processing.

Q2. A) 1101

• Correct: 13 in binary is 1101.
• Incorrect: 1110 = 14, 1001 = 9, 1010 = 10.

Q3. D) It is shorter and easier to read

• Correct: Hex compresses long binary strings into fewer digits, improving readability.
• Incorrect: Hex is not more accurate, nor better for calculations inside the machine.

Q4. B) 157

• Correct: 10011010 = 128 + 16 + 8 + 4 + 1 = 157.
• Incorrect: Other options result from incorrect conversions.

Q5. A) F0

• Correct: 1111 = F, 0000 = 0 → F0.
• Incorrect: 0F = 00001111, A0 = 10100000, FF = 11111111.

Q6. B) 4

• Correct: Each hex digit represents 4 bits.
• Incorrect: 2, 6, and 8 are not valid groupings for hexadecimal conversion.

Q7. B) The value is doubled

• Correct: Logical left shift multiplies the binary number by 2.
• Incorrect: Right shifts divide; zeros are added at the right, not left.

Q8. A) 11111111

• Correct: Each bit pair is 1 (1+0 or 0+1) → full byte of 1s.
• Incorrect: Other results are from incorrect addition or carry errors.

Q9. C) When result exceeds the max value storable in bits

• Correct: Overflow occurs when total exceeds the binary range for the set bit width.
• Incorrect: Subtraction or addition of zeros does not cause overflow.

Q10. B) G

• Correct: Valid hex digits are 0–9 and A–F only.
• Incorrect: D, 9, and B are all within the valid hex range.

Q11. C) FF

• Correct: F = 15, so FF = 15×16 + 15 = 255.
• Incorrect: EE = 238, F1 = 241, 1A = 26.

Q12. A) 00111100

• Correct: 3 = 0011, C = 1100 → 00111100.
• Incorrect: Other combinations mismatch the correct bit patterns.

Q13. A) 00001100

• Correct: 00110000 → right shift 2 bits → 00001100.
• Incorrect: Other answers do not follow correct bit shifting logic.

Q14. A) 11111111

• Correct: -1 in 8-bit two’s complement = invert 00000001 → 11111110 + 1 → 11111111.
• Incorrect: Others are incorrect representations of -1.

Q15. B) 11101110

• Correct: +18 = 00010010 → invert = 11101101 → add 1 = 11101110.
• Incorrect: Other options skip steps or add wrong.

Q16. C) -128 to +127

• Correct: 8-bit two’s complement has this exact range.
• Incorrect: Others are off by 1 or reversed.

Q17. C) It is always 1

• Correct: The MSB (most significant bit) is 1 for all negative two’s complement numbers.
• Incorrect: It is not ignored and isn’t used for parity.

Q18. D) Adding 1

• Correct: After bit inversion, you add 1 to complete two’s complement conversion.
• Incorrect: The process does not involve multiplying or subtracting from 255.

Q19. D) Hexadecimal

• Correct: Hex = base 16.
• Incorrect: Decimal = 10, Binary = 2, Octal = 8.

Q20. A) D7

• Correct: 1101 = D, 0111 = 7 → D7.
• Incorrect: Other options mismatch the binary groups.