Page 24 - TP_iPlus_V2.1_Class7
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There are four types of number systems, which are as follows:
1. Decimal number system 2. Binary number system
3. Octal number system 4. Hexadecimal number system
The decimal number system is commonly used, while computers use the binary number system.
Additionally octal and hexadecimal number systems are also used in computing.
Decimal Number System
A number system that uses 10 digits from 0 to 9, is known as the decimal number system. The
base of the decimal number system is 10. It is also known as the base-10 system.
In the decimal number system, 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 place value of the digits according to position and weight is as follows:
Position 3 2 1 . -1 -2
Weight 10 2 10 1 10 0 10 -1 10 -2
In simple words, the successive position to the left of the decimal point represents units, tens,
hundreds, thousands, and so on.
The value of a 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 right-most
digit of the number has the lowest weight. This digit is called 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
Real Value of each digit 10 1 2 x 10 1 20
Result 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.
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iPlus (Ver. 2.1)-VII

