Computer Science and Information Technology Trishna Knowledge Systems. Digital Logic -Number System Example No - 39

Question

Example 39: (36x 70)₁₀ is 10’s complement of (yzyz0)₁₀ Then values of x, y, z are?

(A) 4, 5, 2

(B) 4, 6, 3

(C) 3, 6, 3

(D) 3, 5, 4

Explain ….

Solution: (C)

Answer 1

The 10’s Complement of (yzyz0)₁₀ is (36x 70)₁₀.

 

Let’s calculate the 10’s complement of (36x 70)₁₀ by standard method & then we will compare.

For calculation of 10’s complement, we have to find 9’s complement first.

 

NOTE : If given number is written in base 2 & we are calculating 1’s complement then we have to subtract

the given number from the highest possible number, which is putting all 1 in all bits. 

If given number is written in base 10 & we want to calculate the 9’s complement then we have to

subtract the given number from the highest possible number, which is putting all 9 in all bits.

If given number is written in base 16 & we want to calculate the 15’s complement then we have to

subtract the given number from the highest possible number, which is putting all 15(F) in all bits.

 

NOTE : If given number is written in base 2 & we are calculating 2’s complement then simply add 1 to

the 1’s complement.

If given number is written in base 10 & we are calculating 10’s complement then simply add 1 to

the 9’s complement.

If given number is written in base 16 & we are calculating 16’s complement then simply add 1 to

the 15’s complement.

 

The 9’s complement of given number is given by :

 

 

Now, let’s calculate the 10’s complement of given number : 

Now, compare the our 10’s complement with the given 10’s complement which is (36x 70)₁₀.

On comparing, we get,

9 – y = 3 

$\therefore$  y = 6

 

9 –  z = 6

$\therefore$  z = 3

 

x = 9 – y

x = 9 – 6

$\therefore$  x = 3

 

So, x = 3, y = 6, z = 3

Option C, is correct answer.