Digital-GrandTest1-Q4

+2 votes

In a base 'b' number system [ 54/4]_b = (13)_b. The value of b is:

asked Jun 19 in Digital by gbmentor (14,390 points)
reshown Jun 20 by gbmentor

3 Answers

+2 votes
 
Best answer

Answer: 8

First convert in base 10 both side.
-> 5b+4/4=b+3
-> 5b+4=4b+12
-> b=8
 

As a check,

(54)8 =5.8+4=44  in base 10, also (4)8=(4)10 .  Hence LHS= 11 in base 10. 

while (13)8= (8+3) = (8+3) =11 in base 10 as well. 

answered Jun 20 by tskukrejakapil7 (1,800 points)
selected Jun 21 by gbmentor
0 votes
Here first convert in base 10

5b+4/4=b+3

5b+4=4b+12

b=8

8 is correct one .
answered Jun 20 by tsnikhilsharmagate2018 (17,270 points)
+1 vote

\frac{5\times b+4\times b^0}{4\times b^0} = 1\times b+3\times b^0

5b+4 = 4(b+3)

so, b = 8 is right value 

answered Jun 20 by 23rishiyadavpro20 (6,560 points)
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