Page 24 - Trackpad_ipro 4.1_Class7
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There are four types of number systems:
1. Decimal Number System 3. Octal Number System
2. Binary Number System 4. Hexadecimal Number System
The Decimal Number System is commonly used in everyday life, but computers use the Binary
Number System. Additionally, computers also utilise the Octal and Hexadecimal Number Systems.
Decimal Number System
The Decimal Number System is a standard number system for denoting numbers. It consists
of ten digits from 0 to 9. Only these digits can be used to represent any numeric value in the
Decimal Number System. Hence, the base of the Decimal Number System is 10. The Decimal
Number System is the most widely used number system. The value represented by the individual
digit depends on the weight and position of the digit.
In the Decimal Number System:
The position of the first digit to the left of the decimal point is 0.
The position of the second digit to the left of the decimal point is 1.
Similarly, the position of the first digit to the right of the decimal point is -1.
The position of the second digit to the right of the decimal point is -2, and so on.
The place value of the digits according to position and weight is as follows:
Position 2 1 0 -1 -2
.
Weight 10 2 10 1 10 0 10 -1 10 -2
The value of a number is determined by multiplying the digits by the weight of their position and
adding the results. This method is known as the expansion method. The right-most digit of the
number has the lowest weight. This digit is called the Least Significant Digit (LSD). The left-most
digit of a number has the highest weight. This digit is called the Most Significant Digit (MSD). The
digit 7 in the number 724 is the most significant digit, and 4 is the least significant digit.
The table below illustrates the positional weight of the decimal number (724)₁₀:
Place Value Weights Real Value of Each Digit Result
Hundreds 10 2 7 x 10 2 700
Tens 10 1 2 x 10 1 20
Units 10 0 4 x 10 0 4
In this table:
The hundreds place has a weight of 10² (100), so the real value is 7 × 100, resulting in 700.
The tens place has a weight of 10¹ (10), so the real value is 2 × 10, resulting in 20.
The units place has a weight of 10⁰ (1), so the real value is 4 × 1, resulting in 4.
Adding these results together gives the total value of 724.
22 iPro (Ver. 4.1)-VII

