What does the word complement means in mathematics?

Answer 1

The "complement" of a number is another number in which each digit, when added to the corresponding digit in the original number, will add up to the largest digit of the base in which the number is expressed.

That sounds far more complicated than it really is. It's easier to understand by working through it. For example, take the decimal number "1976". The complement of 1976 would be another number which, when added to 1976, gives you the value 9999. In other words, each digit, added to it's corresponding digit in the complement, should total 9. So the complement of 1976 would be 8023.

Perhaps a better example would be the number 9876543210. It's complement would be 0123456789. If you add the two numbers together, you'd get 9999999999.

It is important to note though, that the complement of a number will differ depending on the base number is expressed in. For example, take the number 100 in decimal. It's complement is 099. If we express that number in binary however:

1100100

it's complement would be:

0011011

which, converted back to decimal, gives us the value 27. In other words, the value of a number's complement depends on the base in which the number is expressed.