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 Base Sytem Practice Quiz (5 Questions)

Number-System
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 Base Sytem Practice Quiz (5 Questions)

Base System Made Easy | Digits, Conversions & Number Formation

🔢 Base Sytem Practice Quiz (5 Questions)

Understand how numbers are formed using different digits in different bases. This is essential for CAT, SSC, Banking, and other competitive exams.

📝 Base System Practice Quiz (5 Questions)

1. What is the decimal value of \( (1021)_3 \)?
\( 1 \times 3^3 + 0 \times 3^2 + 2 \times 3^1 + 1 \times 3^0 = 27 + 0 + 6 + 1 = \boxed{34} \)
2. Which of the following numbers is not valid in base 5?
(a) 431
(b) 502
(c) 134
(d) 210
Option (b) 502 is invalid because 5 is not allowed in base 5.
3. Convert \( (2A)_\text{16} \) to decimal.
\( 2 \times 16^1 + A \times 16^0 = 2 \times 16 + 10 = \boxed{42} \)
4. Find the largest 2-digit number in base 7.
Largest 2-digit number = \( 7^2 - 1 = \boxed{48} \)
5. Which base allows the number \( (238)_x \) to be valid?
The highest digit is 8. So, base must be \( > 8 \). So minimum valid base = \boxed{9}
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