Page 12 - TP_Pluse_V2.2_Class_7
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Let us first learn how to form binary numbers.
To understand how to form binary numbers, note that the binary system uses only two digits: 0 and 1,
giving it a base of 2. Each digit, or bit, can be either 0 or 1. Binary digits combine to represent various
quantities, such as 1001. In binary, the positional value of each digit is twice the place value or face
value of the digit to its right. The weight of each position in a binary number is a power of 2.
The place value of the digits according to position and weight is as follows:
Position 3 2 1 0 –1 –2
.
Weights 2 3 2 2 2 1 2 0 2 –1 2 –2
Octal Number System
The octal number system consists of eight digits from 0 to 7. Hence, the base of octal number system
is 8. In this system, the position of each digit represents a power of 8. Any digit in this system is always
less than 8. Octal number system is used as a shorthand representation of long binary numbers. The
number (841) is not valid in this number system as 8 is not a valid digit.
8
The place value of the digits is determined by their position and weight as follows:
Position 2 1 0 -1 -2
.
Weights 8 2 8 1 8 0 8 -1 8 -2
Hexadecimal Number System
The hexadecimal number system consists of 16 symbols from 0 to 9 and A to F. The letters A to F
represent decimal numbers from 10 to 15. The base of this number system is 16. Each digit position
in hexadecimal number system represents a power of 16. For example, the number (764) is a
16
valid hexadecimal number. This number system provides shortcut method to represent long binary
numbers.
The place value of the digits is determined by their position and weight as follows:
Position 2 1 0 -1 -2
.
Weights 16 2 16 1 16 0 16 -1 16 -2
DECIMAL TO BINARY CONVERSION
To convert a decimal number into a binary number, follow these steps:
Step 1: Divide the decimal number by 2 (the base of the binary number system).
Step 2: Note down the quotient and the remainder.
Step 3: Divide the quotient obtained again by 2 and note down the resulting quotient and remainder.
Step 4: Repeat the procedure till you reach a quotient less than 2.
Step 5: List the last quotient and all the remainders (moving from bottom to top). You will get your
binary number.
10 Plus (Ver. 2.2)-VII

