Binary number double the number to be converted, record if the result is at least 1, and then throw away the integer part. For example, formula_10, in binary, is: Thus the repeating decimal fraction 0... is equivalent to the repeating binary fraction 0... . Or for example, 0.1, in binary, is: This is also a repeating binary fraction 0.0... . It may come as a surprise that terminating decimal fractions can have repeating expansions in binary. It is for this reason that many are surprised to discover that 0.1 + ... + 0.1, (10 additions) differs from 1 in floating point arithmetic.
Universal binary means to ease the transition from the existing PowerPC architecture to systems based on Intel processors, which began shipping in 2006. Universal binaries typically include both PowerPC and x86 versions of a compiled application. The operating system detects a universal binary by its header, and executes the appropriate section for the architecture in use. This allows the application to run natively on any supported architecture, with no negative performance impact beyond an increase in the storage space taken up by the larger binary. Starting with Mac OS X Snow Leopard, only Intel-based Macs are supported, so software that specifically depends