( 11100 ) 2 = ( 1001 ) x . What is the value of x? Options: A . &nbsp 4 B . &nbsp 5 C . &nbsp 3 D . &nbsp 10 E . &nbsp None of these

(11100)2=(1001)x. What is the value of x?

Question

$(11100)_{2} = (1001)_{x}$ . What is the value of x?

Answer: Option C
:
C

$(11100)_{2} = 0 + 0 + 2^{2} + 2^{3} + 2^{4} = 28$

$(1001)_{x} = x^{0} + x^{3} = 1 + x^{3}$

$1 + x^{3} = 28 = 27 + 1 = 3^{3} + 1, x = 3.$

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