Decimal to Fixed Point Binary Converter Calculator
Decimal to fixed-point binary conversion is the process of representing decimal numbers in binary form with a fixed number of fractional bits.
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Learn about Decimal to Fixed Point Binary Converter
Binary is a number system that only consists of 2 digits: 0 and 1 (Unlike our normal base 10 system, which consists of 10 digits from 0 - 9.). In binary, these 'digits' are known as bits. The binary number system is used by computers to reflect the on (1) and off (0) states of a transistor. Although binary may look odd at first, reading binary numbers is straightforward. It is a positional system, so every bit is raised to the power of 2 based on its position in the number. This starts from the rightmost bit (also called the least significant bit or LSB) with the position index of 0 and goes up from there. With binary, you can also represent fractions. A binary number can be separated by a radix point, with the left side of the point representing the integer part of the number, and the right side representing the fractional part of the number.
Decimal numbers can be converted to binary with a straightforward process. Anytime you want to keep a value within a certain set of numbers, you use the mod operator to get the remainder of a division operation between the two numbers. A good use case for example is to find what day of the week it'll be after an arbitrary amount of day's has passed, let's say 293. To find what day of the week it'll be, you already know that there are 7 days in a week (0 being Sunday...6 being Saturday), so we want to keep the value 293 within 7. Therefore, the operation will be 293 % 7 = 6, meaning the 293 day will fall on the 6th day of the week, which is Saturday. A similar algorithm is applied here. If we want to convert a decimal number into base 2, we have to keep it mod 2, so that it always maps to valid bits. However, we will get the integer quotient for each division operation and keep dividing it by 2, up until the quotient is equal to 0. When it comes to the fractional portion of the number, we do the opposite. Multiply the fractional portion by 2, and for each fractional portion of the result, we will keep multiplying until this portion gets to 0. The integer quotient of each operation will be appended to our answer. For example, let's walk through converting the decimal number 19.59375 into binary.
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