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Given that $(292)_{10} = (1204)_x$ in some number system $x$. The base $x$ of that number system is

  1. 2
  2. 8
  3. 10
  4. None of the above
in Digital Logic by Veteran (103k points)
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2 Answers

+4 votes
Best answer

(292)10=(1204)x

 2*10+ 9*10 + 2 = x+ 2*x2 + 0 + 4

200 + 90 + 2 = x3 + 2x2 + 4

x3 + 2x2 - 288 = 0 

solution for x = 6

none of the option satisfy the equation. 

by Veteran (62.5k points)
selected by
+4 votes

(1204) x = 1*x 3 + 2* x 2 + 0 * x + 4 = x3+2x2+4=292

x3+2x2=288

x2(x+2) = 288

//Rather than solving x, it will be easier to check given options. In time stringent exams, this approach will behelpful

A. 2 2 (2+2) = 4* 6=24 ≠ 288

B. 8 2 (8+2) =64*100 =6400≠ 288

C. 10 2 (10+2) =100*12 =1200 ≠ 288

answer (D)

by Boss (32.2k points)
Answer:

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