ARITHMETICAL COMPLEMENT Meaning and
Definition
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The arithmetical complement refers to a mathematical concept that involves finding the value that, when added to a given number, yields a specific result. It is calculated by subtracting a given number from a specific base or reference number. The arithmetical complement is often used in number systems where a specific base is adopted, such as binary or hexadecimal.
In binary arithmetic, the arithmetical complement is computed by subtracting the given binary number from a base number consisting of all ones. For example, in a binary system with a base of 1111, the arithmetical complement of the number 1010 would be 0101. This calculation effectively flips all the bits in the original number, transforming zeros into ones and ones into zeros.
Similarly, in decimal arithmetic, the arithmetical complement is evaluated by subtracting the given decimal number from a base number consisting of all nines. For instance, in a decimal system with a base of 9999, the arithmetical complement of the number 4721 would be 5278. This computation involves subtracting each digit of the original number from nine.
The arithmetical complement facilitates various mathematical operations, such as subtraction and division, within number systems that adopt a specific base. It enables transformations of negative numbers, carries, and borrows in arithmetic calculations, and contributes to the overall understanding and manipulation of numbers in such systems.
Etymology of ARITHMETICAL COMPLEMENT
The word "arithmetical" derives from the Latin word "arithmetica", which comes from the Greek word "arithmētikē" meaning "the art of numbers". Both Latin and Greek words ultimately trace back to the Greek word "arithmos" meaning "number".
The word "complement" originates from the Latin word "complementum", which comes from the Latin verb "complēre" meaning "to fill up" or "to complete". It is formed from the combination of the prefix "com", indicating "together" or "intensive", and the verb "plēre" meaning "to fill".
Therefore, the etymology of the term "arithmetical complement" can be understood as the "number completion" or the "filling up of numbers" in the context of arithmetic.
