M. Amer Iqbal Qureshi
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- Điều hướng trang này:
- Binary to decimal number conversion
- Hexadecimal to decimal number conversion
| Number system conversion
Binary number system is the most commonly used and decimal system is the most understandable while hexadecimal system is somewhere between them. Therefore, it is very important to learn how to convert numbers from one number system to another, i.e. how to turn series of zeros and units into values understandable for us. Binary to decimal number conversion Digits in a binary number have different values depending on their position in that number. Additionally, each position can contain either 1 or 0 and its value may be easily determined by its position from the right. To make the conversion of a binary number to decimal it is necessary to multiply values with the corresponding digits (0 or1) and add all the results. The magic of binary to decimal number conversion works...You doubt? Look at the example: 110 = 1*2^2 + 1*2^1 + 0*2^0 = 6 It should be further noticed that for decimal numbers from 0 to 3 it is enough to have two binary digits. For greater values, new binary digits must be added. Thus, for numbers from 0 to 7 it is enough to have three digits, for numbers from 0 to 15- four digits etc. Simply speaking, the largest binary number consisting of n digits is obtained when the base 2 is raised by n. The result should be afterwards subtracted by 1. For example, if n=4: 2^4 - 1 = 16 - 1 = 15 Accordingly, using 4 binary digits it is possible to represent decimal numbers from 0 to 15, including these two digits, which amounts to 16 different values in total. Hexadecimal to decimal number conversion In order to make conversion of a hexadecimal number to decimal, each hexadecimal digit should be multiplied with the number 16 raised by it’s position value. For example: Hexadecimal to binary number conversion It is not necessary to perform any calculation in order to convert hexadecimal number to binary number system. Hexadecimal digits are simply replaced by the appropriate four binary digits. Since the maximal hexadecimal digit is equivalent to decimal number 15, it is needed to use four binary digits to represent one hexadecimal digit. For example: tải về 3.06 Mb. Chia sẻ với bạn bè của bạn:
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