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Number System: Complements

Here we are going to calculate (r - 1)’s complement and r’s complement for all base number systems.

How to calculate (r – 1)’s complement

Subtract all digit by (r – 1) – highest digit

For binary number:

Subtracting the all digit by (r – 1) then we will get opposite digit i.e. 1 is 0 and 0 is 1

For Octal:

For Decimal

For Hexadecimal

Now, r’s Complement

Process: First find (r – 1)’s complement then add 1 with LSB of digit then get r’s complement

For Octal

For Decimal

For Binary

Directly we can find 2’s complement of binary number:

From the LSB of digit left all zero until the first 1 appears, when got first 1, keep it as it is and complement the remaining part i.e. 1 to 0 and 0 to 1

Let 

Let

Question:

Answer:

So, first we calculate 7’s complement then by adding 1, we got 8’s complement

So, we should convert 8 to corresponding octal

Correct was