Question:
Consider the expression (xxx)b = (62)b , where b is the base and x is any digit in base b. Find the value of (b + x).
Consider the expression (xxx)b = (62)b , where b is the base and x is any digit in base b. Find the value of (b + x).
Updated On: Aug 21, 2024
- 5
- 12
- 10
- 7
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The Correct Option is D
Solution and Explanation
(xxx)b = x(b2 + b1 + b0)10
x(b2 + b1 + b0)10 = (62)10
x(b2 + b1 + b0)10 = (62)10
x = 2 or 31
But x is a digit. So, it cannot be 31; x must be 2.
(b2 + b1 + b0)10 = (31)10 = (52 + 51 + 1)10 = (52 + 51 + 50)10
b = 5
So, (b + x) = (5 + 2) = 7
So, the correct option is (D) : 7.
x(b2 + b1 + b0)10 = (62)10
x(b2 + b1 + b0)10 = (62)10
x = 2 or 31
But x is a digit. So, it cannot be 31; x must be 2.
(b2 + b1 + b0)10 = (31)10 = (52 + 51 + 1)10 = (52 + 51 + 50)10
b = 5
So, (b + x) = (5 + 2) = 7
So, the correct option is (D) : 7.
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