Binary Numbers Conversion Formula

Dezimalzahlen in Binärzahlen umwandeln und Binärzahlen in Dezimalzahlen
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What are Binary Numbers?

Binary numbers are a number system that uses only two digits, 0 and 1. It is a fundamental concept in the field of computer science and digital electronics. In binary, each digit represents the power of two, with the rightmost digit representing 2^0, the next digit representing 2^1, and so on.

Why Convert Binary Numbers?

Binary numbers are not commonly used in everyday life, but they are essential in computer programming and digital electronics. For example, when working with computer hardware or software, you may need to convert binary numbers to decimal numbers and vice versa. Knowing how to convert binary numbers is a necessary skill in these fields.

Binary to Decimal Conversion Formula

To convert a binary number to a decimal number, you can use the following formula: decimal = (bn * 2^n-1) + (bn-1 * 2^n-2) + … + (b2 * 2^1) + (b1 * 2^0) Where bn is the nth digit of the binary number, and n is the number of digits in the binary number. For example, to convert the binary number 1101 to decimal, you can use the formula: decimal = (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0) = 13

Decimal to Binary Conversion Formula

To convert a decimal number to a binary number, you can use the following formula: binary = (decimal / 2^n) % 2 Where n is the number of digits in the binary number. For example, to convert the decimal number 13 to binary, you can use the formula: binary = (13 / 2^3) % 2 = 1 binary = (13 / 2^2) % 2 = 1 binary = (13 / 2^1) % 2 = 0 binary = (13 / 2^0) % 2 = 1 Therefore, the binary representation of the decimal number 13 is 1101.

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Conclusion

In conclusion, understanding how to convert binary numbers is a crucial skill in the field of computer science and digital electronics. The formulas for converting binary to decimal and decimal to binary are relatively simple to understand and can be useful in a variety of applications. By following the formulas outlined in this article, anyone can convert binary numbers with ease.

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