CAT 2000 | Question: 108

Question

Convert the number $1982$ from base $10$ to base $12.$ The result is

• A. $1182$
• B. $1912$
• C. $1192$
• D. $1292$

Comments

Convert base $12$ to base $10$

I get $1192$

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Can you please share your answer steps?

Thanks,

Regards Sumanth

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see my comment.

Try to convert base $12$ to base $10$.

Go through all the options.

You will easily get the correct answer.

i.e.$(1192)_{12}$--------$>(1982)_{10}$

Answer 1

1192

Answer 2

3.1192

Answer 3

Answer -1192

To convert an integer to base b, divide it by b. The remainder is the ones place.

convert 1982 to base 12 ,first 1982 divide by 12 that gives quotient –  165 and remainder-  2 So the number ends in a 2

again previous quotient  divide by base 12 , 165 divide by 12 that gives quotient –  13 and remainder-  9 So the number ends in a 92

again previous quotient  divide by base 12 , 13 divide by 12 that gives quotient –  1 and remainder-  1 So the number ends in a 192

Finally, 1 is less than 12 so its representation is just 1,

so result is 1192

Answer 4

To convert $(1982)_{10}$ to base -12:

$(1982)_{10}\rightarrow (1192)_{12}$

Option (C) is correct.