Question

How does one obtain the complementary hexadecimal value for a given input ?

This could be a bit more generic, i.e. having an array of X possible values, how do you convert a random array like arr[x] –> arr[arr.length – arr.indexOf(x)].

Please ignore the syntax.

Answer 1

The following code snippet will find 16 complement of hexadecimal number:

BigInteger subtrahend = new BigInteger("2D", 16); 
// input, you can take input from user and use after validation
char[] array = new char[subtrahend.toString(16).length()];
// construct a character array of the given length
Arrays.fill(array, 'F');
// fill the array by F, look at the first source there the FF is subtracted by 2D
BigInteger minuend = new BigInteger(new String(array), 16);
// construct FFF... Biginteger of that length
BigInteger difference = minuend.subtract(subtrahend);
// calculate minus
BigInteger result = difference.add(BigInteger.ONE);
// add one to it
System.out.println(result.toString(16));
// print it in hex format

Hope this will help you. Thank you.

Source:

1. Binary and Hexadecimal Arithmetic
2. Digital Principles and Logic Design

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First find the 15’s complement of the given input by subtracting it from the number FF… which is of the same length of the input. Then add 1 to it.