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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.
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Hexadecimal Number System
The hexadecimal number system consists of 16 digits 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 valid hexadecimal
16
number. It is different from (764) which is seven hundred and sixty four. This number system provides
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shortcut method to represent long binary numbers.
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.
Look at the given examples to understand the conversion better.
Example 1: Convert the decimal number 26, i.e., (26) to binary.
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2 26
2 13 0 The binary equivalent of (26) is 11010
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2 6 1 In other words, (26) = (11010) 2
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2 3 0
1 1
Start listing the last quotient and all the
remainders from here.
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