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 EasyConvert the following binary number to decimal: 01011₂Explanation01011₂ = 0×16 + 1×8 + 0×4 + 1×2 + 1 = 11.
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Q2 EasyConvert hexadecimal A to decimal.ExplanationIn hexadecimal, the digit A represents decimal 10.
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Q3 EasyWhat decimal number is equivalent to the binary numeral 1010 when each place value is expanded in base two?Explanation1010₂ = 1×8 + 0×4 + 1×2 + 0×1 = 10.
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Q4 EasyWhen the decimal integer 13 is converted to binary notation, which four-digit binary string is the correct result?Explanation13 = 8 + 4 + 1 = 1101₂.
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Q5 MediumConvert the following binary number to octal: 010111100₂ExplanationGroup bits in threes from the right: 010 111 100 → 2 7 4 → 274₈.
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Q6 MediumConvert binary 111111110010 to hexadecimal.ExplanationGroup in fours from the right: 1111 1111 0010 → F F 2 → FF2₁₆.
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Q7 MediumConvert the decimal number 187 to 8-bit binary.Explanation187 = 128 + 32 + 16 + 8 + 2 + 1 = 10111011₂.
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Q8 MediumConvert the binary number 1001.0010₂ to decimal.ExplanationInteger part: 8 + 1 = 9. Fraction: 0×1/2 + 0×1/4 + 1×1/8 + 0×1/16 = 1/8 = 0.125. Total = 9.125.
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Q9 MediumWhat is the decimal value of the octal number 17 when written in base ten?Explanation17₈ = 1×8 + 7 = 15 in decimal.
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Q10 MediumA placement question asks you to express the decimal number 25 in base eight; what is the correct representation?Explanation25 ÷ 8 = 3 remainder 1; 3 ÷ 8 = 0 remainder 3 → 31₈.
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Q11 MediumWhat binary sum do you obtain when you add the binary numbers 111 and 101 according to base-2 rules?Explanation111₂ = 7 and 101₂ = 5. Sum = 12 = 1100₂.
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Q12 MediumIf you convert the decimal number 20 into binary, which five-bit binary expression is correct?Explanation20 = 16 + 4 = 10100₂.
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Q13 MediumWhat decimal equivalent does the octal number 25 represent when converted to base ten?Explanation25₈ = 2×8 + 5 = 21.
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Q14 HardWhat is the decimal value of the base-five number 234 when expanded using powers of five?Explanation234₅ = 2×25 + 3×5 + 4 = 50 + 15 + 4 = 69.
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DS1 Easy
What is the decimal value of the binary number N?
Statement IThe binary number N is equal to 1010₂.
Statement IIThe binary number N contains exactly four bits.
Explanation1010₂ = 1×8 + 1×2 = 10. Knowing only the bit count does not fix the digit pattern. -
DS2 Easy
What is the decimal equivalent of the octal number 25₈?
Statement IThe leading digit of the octal number is 2.
Statement IIThe units digit of the octal number is 5.
ExplanationTogether the digits identify 25₈ = 2×8 + 5 = 21. Neither digit alone determines the full value.
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DS3 Medium
What is the base-eight representation of the decimal number 25?
Statement IWhen 25 is divided by 8, the remainder is 1.
Statement IIWhen 25 is divided by 8, the quotient is 3.
ExplanationTogether: 25 = 8×3 + 1 → 31₈. Neither the remainder nor the quotient alone gives the full octal form. -
DS4 Medium
What is the sum of the binary numbers 101₂ and 110₂?
Statement IBoth numbers are written in base 2.
Statement IIThe sum of the two numbers is greater than 1000₂.
ExplanationKnowing the base alone or that the sum exceeds 8 does not compute the exact result. 101₂ + 110₂ = 1011₂.