METHOD OF COMPLEMENTS Meaning and
Definition
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The method of complements is a mathematical technique used in arithmetic to perform subtraction quickly and efficiently. It involves exploiting the relationship between addition and subtraction by converting the subtracted number and the result into their respective complements. In this method, the complement of a number is defined as the difference between that number and the base of the number system being used.
The procedure of the method of complements is as follows. First, the number to be subtracted is converted into its complement by subtracting it from the base. Then, the original number is also converted into its complement using the same process. The resulting complements are added together. Finally, the carry from the leftmost position, if any, is added to the sum. The final result obtained is the complement of the desired difference. To obtain the correct difference, the result is then converted back into the original number by subtracting it from the base.
The method of complements is often used in computers to perform subtraction operations efficiently. It eliminates the need for separate subtraction circuitry by utilizing the existing addition circuitry. This technique also simplifies the process of borrowing and allows for easy implementation of subtraction in binary systems. Additionally, the method of complements can be applied not only to whole numbers, but also to fractions and decimals, providing a flexible and versatile approach to subtraction in various number systems.
