Question

Q. Find the 11's complement of following numbers:
(i) (935) base12
(ii) (267) base12
​

Answer 1

Answer:

(i) 792

(ii) 1460

Step-by-step explanation:

base n=((n^k)-1)-x

n=base

x=given number

k=total no. of digit

Answer 2

11's complement of $935_{12}$ is $\bf \red{286_{12}}$.

11's complement of $267_{12}$ is $\bf \red{954_{12}}$.

Given:

• (i) $935_{12}$
• (ii)$267_{12}$

To find:

• Find 11's complement of the given numbers.

Solution:

Concept to be used:

• When a number in 'r' index, that means there are total r symbols.
• So, when (r-1)'s complement be taken, the individual digits of number is subtracted by the largest symbol.

For example in decimal number system, its bâse is 10; symbols of decimal number system are (0,1,2,3,4,5,6,7,8,9).

So, when 9's complement is taken then every digit is subtracted by 9.

Case 1:

(i) $935_{12}$

As the symbols in 12 base system are (0,1,2,3,4,5,6,7,8,9,A,B) and highest symbol is 'B', which means '11'.

So, subtract each digit from 11, will give 11's complement.

$11 - 9 = 2 \\ 11 - 3 = 8 \\ 11 - 5 = 6$

Thus,

11's complement of $935_{12}$ is $\bf {286_{12}}$.

Case 2:

(ii) $267_{12}$

Find 11's complement of $267_{12}$

Using the same method,

$11 - 2 = 9 \\ 11 - 6 = 5 \\ 11 - 7 = 4$

Thus,

11's complement of $267_{12}$ is $\bf 954_{12}$.

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