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Number System sneha
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Topics to be discussed Number System Types of Number System
Types of positional number system Binary to Decimal Octal to Decimal Hexadecimal to Decimal Decimal to Binary Octal to Binary Hexadecimal to Binary Decimal to Octal
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Cont… Decimal to Hexadecimal Binary to Octal Binary to Hexadecimal
Octal to Hexadecimal Hexadecimal to Octal Exercise – Convert ...
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Number System A number system defines how a number can be represented using distinct symbols. A number can be represented differently in different systems. For example, the two numbers (2A)16 and (52)8 both refer to the same quantity, (42)10, but their representations are different. Several number systems have been used in the past and can be categorized into two groups: positional and non- positional systems. Our main goal is to discuss the positional number systems, but we also give examples of non- positional systems.
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Types of Number System Two types of Number System Positional No System
Non- Positional No System
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Types of positional number system
Various positional number system: Binary number system Decimal number system Octal number system Hexadecimal number system
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Conversion Among Bases
The possibilities Decimal Octal Binary Hexadecimal
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Quick Example 2510 = = 318 = 1916 Base
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Binary to Decimal Decimal Octal Binary Hexadecimal
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Binary to Decimal Technique
Multiply each bit by 2n, where n is the “weight” of the bit The weight is the position of the bit, starting from 0 on the right Add the results
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Example Bit “0” => 1 x 20 = x 21 = x 22 = x 23 = x 24 = x 25 = 32 4310
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Octal to Decimal Decimal Octal Binary Hexadecimal
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Octal to Decimal Technique
Multiply each bit by 8n, where n is the “weight” of the bit The weight is the position of the bit, starting from 0 on the right Add the results
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Example 7248 => 4 x 80 = x 81 = x 82 =
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Hexadecimal to Decimal
Octal Binary Hexadecimal
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Hexadecimal to Decimal
Technique Multiply each bit by 16n, where n is the “weight” of the bit The weight is the position of the bit, starting from 0 on the right Add the results
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Example ABC16 => C x 160 = 12 x 1 = B x 161 = 11 x 16 = A x 162 = 10 x 256 = 2560 274810
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Decimal to Binary Decimal Octal Binary Hexadecimal
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Decimal to Binary Technique
Divide by two, keep track of the remainder. If remainder is zero then it track zero If remainder is not zero then it track 1
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Example 12510 = ?2 12510 =
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Octal to Binary Decimal Octal Binary Hexadecimal
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Octal to Binary Technique
Convert each octal digit to a 3-bit equivalent binary representation
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Example 7058 = ?2 7058 =
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Hexadecimal to Binary Decimal Octal Binary Hexadecimal
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Hexadecimal to Binary Technique
Convert each hexadecimal digit to a 4-bit equivalent binary representation
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Example 10AF16 = ?2 A F 10AF16 =
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Decimal to Octal Decimal Octal Binary Hexadecimal
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Decimal to Octal Technique Divide by 8 Keep track of the remainder
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Example = ?8 8 19 2 8 2 3 8 0 2 = 23228
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Decimal to Hexadecimal
Octal Binary Hexadecimal
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Decimal to Hexadecimal
Technique Divide by 16 Keep track of the remainder
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Example = ?16 77 2 16 = D 0 4 = 4D216
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Binary to Octal Octal Decimal Hexadecimal Binary
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Binary to Octal Technique Group bits in threes, starting on right
Convert to octal digits
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Example = ?8 = 13278
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Binary to Hexadecimal Decimal Octal Hexadecimal Binary
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Binary to Hexadecimal Technique Group bits in fours, starting on right
Convert to hexadecimal digits
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Example = ?16 B B = 2BB16
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Octal to Hexadecimal Octal Decimal Binary Hexadecimal
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Octal to Hexadecimal Technique Use binary as an intermediary
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Example 10768 = ?16 E 10768 = 23E16
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Hexadecimal to Octal Octal Decimal Binary Hexadecimal
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Hexadecimal to Octal Technique Use binary as an intermediary
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Example 1 F C 1F0C16 = ?8 1F0C16 =
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Exercise – Convert ... Decimal Binary Octal Hexa- decimal 33 1110101
703 1AF
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Exercise – Convert … Decimal Binary Octal Hexa- decimal 33 100001 41
Answer Decimal Binary Octal Hexa- decimal 33 100001 41 21 117 165 75 451 703 1C3 431 657 1AF
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