Find r and r-1 complement of : (3546) 16 , (11101) 2 , (6564) 8
Answers
Step-by-step explanation:
1) (r-1)'s complement
The (r-1)'s complement of a number in any number system with base r can be found out by subtracting every single digit of a number by r-1.
For Example: In the binary number system, the base is 2. Hence, its (r-1)'s i.e., (2-1 =1)'s complement can be obtained by subtracting each bit from 1, i.e., 1's complement for 001 can also be calculated by subtracting 001 from 111 which will be (111-001) = (110)2.
Similarly, in the octal number system, the base is 8 so its 7's complement can be calculated by subtracting each bit by 7, i.e., 7's complement for 347 in octal number system can be calculated by subtracting 347 from 777 which will yield (777 – 347) = (430)8.
2) r's complement
The r's complement of a non-zero number in any number system with base r can be calculated by adding 1 to the LSB of its (r-1)'s complement.
For Example: In binary number system, 2's complement of 001 can be
calculated by adding 1 to the LSB of its 1'complement (i.e., 110 + 1) = (111)2.
Similarly, in octal number system, 8's complement of 347 can be calculated by adding 1 to the LSB of its 7'complement (i.e., 430 + 1) = (431)8.
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