COMPUTER-NUMBER SYSTEM

[Virtual Presenter] Computer number System Made By Kartavya Jha.

[Audio] Content: 1 What is computer number system? 7 Summary 2Types of number system 3 Decimal to binary conversion 4 Binary to decimal conversion 5Octal to binary conversion 6Hexadecimal to binary s.

[Audio] What is Computer number system A number system helps us show values or quantities with a set of numbers or symbols. In computers number system is the base, for how machines handle, save and share data. Computers use number system to process data It is also used to store data and to communicate data..

[Audio] Types Of Number System 1. Decimal Number System Base: 10 Digits Used: \(0\) to \(9\) Overview: This is the standard, everyday system humans use for counting and math. Each digit's value is determined by its position (place value) in powers of 10. 2. Binary Number System Base: 2 Digits Used: \(0\) and \(1\) Overview: This is the foundational system used by computers and electronic devices. Because computers operate on electronic circuits that only have two states—ON (\(1\)) and O-F-F (\(0\))—all data is translated into binary code..

[Audio] 3. Octal Number System Base: \(8\) Digits used: Eight digits from \(0\) to \(7\). Characteristics: It is used in computer programming as a shorter way to represent large binary numbers, since three binary digits can be compressed into one octal digit. Positional value: Each position represents a power of \(8\). 4. Hexadecimal Number System Base: \(16\) Digits used: Sixteen alphanumeric characters. It uses numbers \(0\) to \(9\) and letters \(A, B, C, D, E, F\) to represent values from \(10\) to \(15\). Characteristics: Heavily used in computer science for memory addressing and defining colors (HTML color codes). Positional value: Each position represents a power of \(16\)..

[Audio] Binary to decimal conversion. for converting binary into decimal, let me tell you how to do that! Pick some binary number, any number; let's take one such as 11001. So write that down on the piece of paper! Now starting from right to left, count powers of two beginning with two raised to the power of zero:2^0, which is just one,2^1 which is 2, then four, then eight, then sixteen, then thirty two, then so on: all you have to do is multiply whatever number you get by two and you have the power of two. And since our number is 11001, you would have: 1 is with 16,1 is with 8,0 is with 4,0 is with 2 and 1 is with 1. Now you must add up every digit times what power of two it belongs with. So for our number, 1 times 16, 1 times eight, 0 times 4, 0 times 2, 1 times one, adding these numbers up we get sixteen plus eight equals twenty four and 24 plus one equals 25. So 11001 binary is 25 decimal. It is as easy as pie and if you can get the trick to it, you'll be able to do it just like anyone can with the internet..

[Audio] Decimal to binary For converting the decimal number 25 into binary (11001) by repeatedly dividing the number by 2 and recording the remainders. The process begins with 25 divided by 2, resulting in a quotient of 12 and a remainder of 1. This is followed by successive divisions (12 by 2 gives 6 with a remainder of 0, then 6 by 2 gives 3 with a remainder of 0, followed by 3 by 2 giving 1 with a remainder of 1, and finally 1 by 2 results in 0 with a remainder of 1). The binary representation is read from the last remainder to the first, resulting in 11001..

[Audio] Octal to binary To convert an octal number (base 8) to a binary number (base 2), replace each octal digit with its 3-bit binary equivalent. For example, the conversions are: 0 →000, 1 → 001, 2 → 010, 3 → 011, 4 → 100, 5 → 101, 6 → 110, and 7 → 111. For instance, \(246_8\) converts to \(010100110_2\), \(35_8\) to \(011101_2\), and \(705_8\) to \(111000101_2\). Simply stack the corresponding binary forms to get your final binary number..

[Audio] Hexa decimal to binary Turning a hexadecimal number into binary involves substituting each hex digit with its corresponding 4-bit binary representation. The hexadecimal to binary conversion utilizes a straightforward mapping which can be summarized in a table form, where hex digits from 0 to F are translated into 4-bit binary sequences. For example, the hex number 2AF can be converted by breaking it into its individual digits: 2, A, and F The binary equivalents of these are 0010, 1010, and 1111, respectively. When combined, these yield the final binary representation: 001010101111. This method applies to both uppercase and lowercase hexadecimal letters..

[Audio] Summary im tired A computer number system is a method for storing and retrieving information, with the most common systems being Decimal, Binary, Octal, and Hexadecimal. Decimal (Base 10) is the everyday counting system (0-9). Binary (Base 2) represents data as 0 seconds and 1 seconds, critical for computer data storage. Octal (Base 8) simplifies Binary by grouping bits into sets of three. Hexadecimal (Base 16) extends counting with values 0-9 and letters A-F, commonly used in coding and graphics for colors and memory addresses..

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