Topic: Digital Circuits
If $(146)_{x}+(313)_{x-2}=(246)_{8},$ then the value of base x is
- A. 5
- B. 6
- C. 7
- D. 9
Answer: C. 7
Explanation: $(146)_{x}+(313)_{x-2}=(246)_{8}$. Converting into common base 10 as $x^{2}+4x+6+3(x-2)^{2}+1(x-2)+3=2\times8^{2}+4\times8+6 \Rightarrow 4x^{2}-7x-147=0 \Rightarrow x=7$.