[PDF] [PDF] Number systems and conversions from one system to another

[PDF] NUMBER SYSTEM CONVERSIONS - ipsgwaliororg

A) Divide the Number (Decimal Number) by the base of target base system (in which you want to convert the number: Binary (2), octal (8) and Hexadecimal (16 )) 

[PDF] Number System Conversion - Tutorialspoint

NUMBER SYSTEM CONVERSION There are many methods or techniques which can be used to convert numbers from one base to another We'll demonstrate 

[PDF] Number systems and conversions from one system to another

Uses 16 symbols: 0, 1, 2, , 9, A, B, C, D, E, F Notes: ▫ When written down, a number may be ambiguous regarding which system it belongs to So we will 

[PDF] 3 Convert a number from one number system to another

for example: we use 10-based numbering system for input and output in digital calculator There are two ways to convert a decimal number to its equivalent quotient of 0 is obtained Note: The binary result is obtained by writing the first

[PDF] NUMBER SYSTEMS

number system, e g , it may be required to convert a decimal number to binary or octal or hexadecimal The reverse is also true, i e , a binary number may be 

[PDF] Number Systems- Binary System

The base or radix of number system determines how many numerical digits the number To convert a decimal number to any other number system, divide the decimal And note down the remainders in the reverse order • To convert from 

[PDF] DECIMAL, BINARY, AND HEXADECIMAL - Washington

Decimal Numbering System Can convert from any base to base 10 Summary Humans think about numbers in decimal; computers think about numbers in 

[PDF] Conversion of Binary, Octal and Hexadecimal Numbers - UCR CS

Replace each hexadecimal digit with the corresponding 4-bit binary string 8B16 = 1000 1011 = 100010112 Page 2 Conversion of Decimal Numbers

[PDF] 1 Number System (Lecture 1 and 2 supplement)

Moreover, we can always convert them from any high-base number system to a Note that since these number systems possess base 2k , all numbers within 

[PDF] 2018-19 Unit 1 Number system full notespdf - Yengage

Binary : 7 3 1 Octal : 111011 001 So, 731, = 1110110012 5 Decimal to Octal Conversion: To convert a decimal number to its octal equivalent, the remainder 

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1520W12(sectionS),Numbersystems&conversionsPage 1 of 3Number systems and conversions from one system to another. The 4 number systems are: Binary [ 2 ] . § Uses 2 symbols: the digits 0 and 1. § Some numbers in this system: 0, 000, 1010. Decimal [ 10 ] § Uses 10 symbols: the digits 0, 1, 2, ... ,9. § Some numbers in this system: 111, 0, 1010. Octal [ 8 ] § Uses 8 symbols: the digits 0, 1, 2, 3, 4, 5, 6, 7. Hexadecimal [ 16 ] § Uses 16 symbols: 0, 1, 2, ...., 9, A, B, C, D, E, F. Notes: § When written down, a number may be ambiguous regarding which system it belongs to. So we will associate a subscript to clear such ambiguities. 1010 in the binary system will be denoted as 1010[!] to distinguish it from 1010 of the decimal system, which would be denoted as 1010[!"]. Similarly, 1010 of the octal system, would be denoted as 1010[!], and 1010 of the Hex system would be denoted as 1010[!"]. Conversions from one system to another. It is possible to convert between any of the number systems. [ 2 ] à [ 10 ] 1010[!]= ?[!"] 1010[!] Based on multiplying with powers of 2. 1010!= 1∗2!+ 0∗ 2!+1∗2!+0∗2!=2!+2!=8+2=10 i.e. 1010[!]=10[!"] [ 10 ] à [ 2 ] 10[!"]=?[!] 10[!"]

1520W12(sectionS),Numbersystems&conversionsPage 2 of 3Based on dividing by 2. Record the quotients and the remainders. Stop diving if quotient is 0, and then take the remainders bottom to top. This would be the binary number. Number Operation Quotient Remainder 10 10 / 2 5 0 5 5/2 2 1 2 2/2 1 0 1 ½ 0 1 Taking the remainders bottom-to-top on the above table forms the number 1010. This would be the binary number that is equal to 10[!"], i.e. 10[!"]=1010[!]. [ 2 ] à [ 8 ] 1010[!]= ?[!] Take chunks of 3 digits from right to left (pad with 0's at the left if there are not enough binary digits), and write the octal digit that corresponds to each chunk. 1010[!]= 001 010 [!]=1[!] 2[!]=12[!]. [ 8 ] à [ 2 ] 12[!]=?[!] Take each octal digit and map it to its binary representative with 3 binary digits. 12[!]→ 001! 010[!]→ 001010[!]=1010 [!] [ 2 ] à [ 16 ] 11010[!]= ?[!"] Take chunks of 4 digits from right to left (pad with 0's at the left if there are not enough binary digits), and write the hex digit that corresponds to each chunk. 11010[!]= 0001 [!]1010 [!]=1[!"] í µ[!"]=1í µ[!"].

1520W12(sectionS),Numbersystems&conversionsPage 3 of 3 [ 16 ] à [ 2 ] 1í µ[!"]=?[!] Take each hex digit and map it to its binary representative with 4 binary digits. 1í µ[!"]=0001 [!]1010[!]=00011010 [!]=11010[!] The diagram below shows all the conversion cases covered above. This means that we can now handle any type of conversion, even conversions between the number systems that are not directly connected on the above diagram. For example, to convert [ 8 ] à [ 10 ], we can convert [ 8 ] à [ 2 ] followed by [ 2 ] à [ 10 ]. Or, to convert [ 8 ] à [ 16 ], we can convert [ 8 ] à [ 2 ] followed by [ 2 ] à [ 16 ]. Etc.

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