GATE | Gate IT 2005 | Question 47

(34.4)₈ × (23.4)₈ evaluates to:

(A)

(1053.6)8

(B)

(1053.2)8

(C)

(1024.2)8

(D)

None of these

Answer: (A)

Explanation:

We convert (34.4)₈ to decimal. = 3 * 8¹ + 4 * 8⁰ + 4 * 8^-1 = 3 * 8 + 4 + 0.5 = (28.5)₁₀
We covert (23.4)₈ to decimal. = 2 * 8¹ + 3 * 8⁰ + 4 * 8^-1 = 2 * 8 + 3 + 0.5 = (19.5)₁₀
Now, (28.5)₁₀ * (19.5)₁₀ = (555.75)₁₀
We convert (555.5)₁₀ to octal. 555 / 8 = 69 , 555 % 8 = 3 69 / 8 = 8 , 69 % 8 = 5 8 / 8 = 1 , 8 % 8 = 0 1 / 8 = 0 , 1 % 8 = 1 
We keep multiplying the decimal part by 8 till it becomes 0. 0.75 * 8 = 6.0 
Thus, (555.75)₁₀ = (1053.6)₈

Thus, option (A) is correct. 

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