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# GATE | Gate IT 2005 | Question 47

• Difficulty Level : Basic
• Last Updated : 28 Jun, 2021

(34.4)8 × (23.4)8 evaluates to

 A) (1053.6)8 B) (1053.2)8 C) (1024.2)8 D) None of these

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.

Please comment below if you find anything wrong in the above post.

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