Published by: Nuru
Published date: 22 Jun 2021
The Decimal Number System is derived from a Latin prefix deci which means 10. So, it consists of ten digits from 0 to 9. These digits can be used to represent any kind of numeric value. The base of the decimal number system is 10. So, it should always be written with subscript 10. However, as it is the most widely used number system, the subscript is usually understood and ignored in written work. The value represented by an individual digit depends on the weight and position of the digit.
Each number in this system consists of digits that are located at different positions. The position of the first digit towards the left side of the decimal point is 0. The position of the second digit towards the left side of the decimal point is 1. Similarly, the position of the first digit towards the right side of the decimal point is -1. The position of the second digit towards the right side of the decimal point is -2 and so on. The magnitude of a number can be considered using absolute value, place value or positional value, top value and base value.
The value of the number is determined by multiplying the digits with the weight of their position and adding the results. This method is known as the expansion method. The rightmost digit of the number has the lowest weight. This digit is called the Least Significant Digit (LSD). The leftmost digit of a number has the highest weight. This digit is called the Most Significant Digit (MSD). Digit 7 in the number 724 is the most significant digit and 4 is the least significant digit.
Simply, 9’s complement of a decimal number is the subtraction of it’s each digit from 9. For example, 9’s complement of decimal number 2005 is 9999 - 2005 = 7994.
10’s complement of a decimal number is 9’s complement of a given number plus 1 to the least significant bit (LSB). For example 10’s complement of decimal number 2005 is (9999 - 2005) + 1 = 7995.