How would the decimal number 1409 be stored

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Reference no: EM133416904

Question: The bfloat16 "brain floating point" format is a 16 bit format used in Google's machine learning and AI software. It is a binary floating point format which is very similar to 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 then only the fraction is stored in memory).

a. What is the approximate decimal precision of a brain floating point? Show all your working.

b. 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 10001001 0110000. Show all your working.

c. Assuming symmetric rounding is used, how would the decimal number 1409 be stored (or approximated) in the bfloat16 format? Show all your working.

Reference no: EM133416904

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