Consider the following equation and find out the base of the number system(radix r):
(143)_r = (25)_r + (43)_r + (11)_r + (20)_r
(A) 5
(B) 6
(C) 7
(D) All of the above


Answer: (B)

Explanation: (143)_r = (25)_r + (43)_r + (11)_r + (20)_r
r² + 4r + 3 = 2r + 5 + 4r + 3 + r + 1 + 2r
r² -5r -6 = 0
(r – 6)*(r + 1) = 0
base of system can not be negative.
That\’s why r = 6
So, option (B) is correct.


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