Practice Questions
Number Bases
In base b, each digit position represents a power of b. Decimal (base 10) is standard; binary (base 2), octal (base 8), and hexadecimal (base 16) appear in aptitude tests.
Conversion
Base to decimal: expand digits × powers of base. Decimal to base: repeated division, collect remainders.
Arithmetic in Other Bases
Add/subtract column-wise with carry when sum ≥ base. Multiplication follows the same rules with base-specific digits.
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Q1 Easy
Binary 1010 equals decimal:
Explanation1010₂ = 1×8 + 0×4 + 1×2 + 0 = 10. -
Q2 Easy
Decimal 13 in binary is:
Explanation13 = 8+4+1 = 1101₂. -
Q3 Medium
Octal 17 equals decimal:
Explanation1×8 + 7 = 15. -
Q4 Medium
Decimal 25 in base 8 is:
Explanation25 ÷ 8 = 3 rem 1, 3 ÷ 8 = 0 rem 3 → 31₈. -
Q5 Medium
Binary 111 + 101 equals:
Explanation7 + 5 = 12 = 1100₂. -
Q6 Easy
Hexadecimal A equals decimal:
ExplanationIn hex, A = 10. -
Q7 Easy
Decimal 7 in binary:
Explanation7 = 4+2+1 = 111₂.
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Q8 Hard
Base-5 number 234 equals decimal:
Explanation2×5² + 3×5 + 4 = 50 + 15 + 4 = 69. -
Q9 Medium
Decimal 20 in binary:
Explanation16+4 = 10100₂. -
Q10 Medium
Octal 25 equals decimal:
Explanation2×8 + 5 = 21. -
Q11 Easy
Binary 1001 in decimal:
Explanation8+1 = 9. -
Q12 Hard
Sum of 12 (decimal) and 5 (decimal) in binary:
Explanation12+5=17 = 10001₂. -
Q13 Hard
Base-3 number 122 equals decimal:
Explanation1×9 + 2×3 + 2 = 9+6+2 = 17. -
Q14 Medium
Decimal 31 in binary:
Explanation16+8+4+2+1 = 11111₂.
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DS1 Easy
What is the decimal value of binary N?
Statement IN = 1010.
Statement IIN has four bits.
Explanation1010₂ = 10. Statement II alone does not give the bit pattern. -
DS2 Medium
What is 25 in base 8?
Statement I25 ÷ 8 leaves remainder 1.
Statement IIThe quotient is 3.
ExplanationTogether: 25 = 8×3 + 1 → 31₈. Neither alone gives the full conversion.
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DS3 Medium
What is the sum of 101 and 110 in binary?
Statement IBoth numbers are in base 2.
Statement IIThe sum exceeds 1000₂.
ExplanationKnowing base 2 alone or that sum > 8 does not compute the exact sum (1011₂). -
DS4 Easy
What is the decimal equivalent of octal 25?
Statement IThe leading digit is 2.
Statement IIThe units digit is 5.
ExplanationTogether identify 25₈ = 2×8 + 5 = 21. Neither digit alone gives the value.