# Convert decimal to 8 bit binary python

So take a number say Then repeat the mod, div process until your number is 0. This will leave you with a list of 1's and 0's in the case of All you have to do now is reverse that number to get the correct binary number: From binary to decimal: This is slightly easier.

For example take binary: Hope you understand how binary and decimal conversions work in theory, so all you need to do now is convert the text explanation above into code. Good luck and have fun. If you get stuck, paste your code using codeblocks and i'll try help point you in the right direction. Here however a possible base may extend beyond just the decimal digits, so it is no longer possible to rely on zero to nine only and their associated character codes, thus the "digit" is now identified by indexing into an array of digits, thereby enabling "A" to follow "9" without character code testing.

The original routine was intended for usages in the hundreds of millions of calls, so this version would be unsuitable! In handling this, the exponent part was added to DD and who knows, the result may produce a zero DD as in " Few numbers are presented with more than sixteen fractional digits, but I have been supplied data supposedly on electric power consumption via the national grid with values such as 1.

It is better to risk one only, at the end. In a more general situation the text would first have to be scanned to span the number part, thus incurring double handling. The codes for hexadecimal, octal and binary formats do not read or write numbers in those bases, they show the bit pattern of the numerical storage format instead, and for floating-point numbers this is very different. Note the omitted high-order bit in the normalised binary floating-point format - a further complication.

Rather than mess about with invocations, the test interprets the texts firstly as base ten sequences, then base two. It makes no complaint over encountering the likes of "" when commanded to absorb according to base two. The placewise notation is straightforward: For example, even though bit processors may address memory sixty-four bits at a time, they may still split that memory into eight-bit pieces. This is called byte-addressable memory. Historically, many CPUs read data in some multiple of eight bits.

A nibble sometimes nybble , is a number composed of four bits. A person may need several nibbles for one bite from something; similarly, a nybble is a part of a byte. Because four bits allow for sixteen values, a nibble is sometimes known as a hexadecimal digit. Octal and hex are convenient ways to represent binary numbers, as used by computers.

Computer engineers often need to write out binary quantities, but in practice writing out a binary number such as is tedious and prone to errors. Therefore, binary quantities are written in a base-8, or "octal", or, much more commonly, a base, "hexadecimal" or "hex", number format. In the decimal system, there are 10 digits, 0 through 9, which combine to form numbers.

In an octal system, there are only 8 digits, 0 through 7. That is, the value of an octal "10" is the same as a decimal "8", an octal "20" is a decimal "16", and so on. In a hexadecimal system, there are 16 digits, 0 through 9 followed, by convention, with A through F. That is, a hex "10" is the same as a decimal "16" and a hex "20" is the same as a decimal "32".

An example and comparison of numbers in different bases is described in the chart below. Each of these number systems are positional systems, but while decimal weights are powers of 10, the octal weights are powers of 8 and the hex weights are powers of To convert from hex or octal to decimal, for each digit one multiplies the value of the digit by the value of its position and then adds the results. Fixed-point formatting can be useful to represent fractions in binary. The number of bits needed for the precision and range desired must be chosen to store the fractional and integer parts of a number.

For instance, using a bit format, 16 bits may be used for the integer and 16 for the fraction. The eight's bit is followed by the four's bit, then the two's bit, then the one's bit. The fractional bits continue the pattern set by the integer bits. This form of encoding cannot represent some values in binary. Even if more digits are used, an exact representation is impossible.

While both unsigned and signed integers are used in digital systems, even a bit integer is not enough to handle all the range of numbers a calculator can handle, and that's not even including fractions. To approximate the greater range and precision of real numbers , we have to abandon signed integers and fixed-point numbers and go to a " floating-point " format. In the decimal system, we are familiar with floating-point numbers of the form scientific notation:. We have a certain numeric value 1.

If we have a negative exponent, that means the number is multiplied by a 1 that many places to the right of the decimal point. The advantage of this scheme is that by using the exponent we can get a much wider range of numbers, even if the number of digits in the significand, or the "numeric precision", is much smaller than the range.

Similar binary floating-point formats can be defined for computers. The IEEE standard specification defines a 64 bit floating-point format with:. Let's see what this format looks like by showing how such a number would be stored in 8 bytes of memory:. Once the bits here have been extracted, they are converted with the computation:.