Problem
Google's machine learning and AI software utilizes the bfloat16 "brain floating point" format, which is a 16-bit format. It is a binary floating point format that closely resembles the single precision IEEE-754 format: 1 bit is allocated for the sign, 8 bits for the exponent with a bias of 127, but only 7 bits are allocated for the fraction (the exponent is always chosen so that the first digit of the mantissa is 1, and only the fraction is stored in memory).
• What is the approximate decimal precision of a brain floating point?
• If the bits are stored in the order: sign, exponent, fraction, and 0 corresponds to a positive sign, then calculate the decimal representation of the number stored as: 1 00001110 0100010.