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(d) Supposing that numbers are truncated (rounded down), what is the maximum absolute rounding error in bfloat16?

(d) Supposing that numbers are truncated (rounded down), what is the maximum absolute rounding error in bfloat16?

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Please answer part D only

4. The bfloat 16 "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? (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 00000110 (c) Given that the largest exponent actually used for numbers is 11111110, what is the largest number that can be expressed as a bfloat 16? 0100010 (d) Supposing that numbers are truncated (rounded down), what is the maximum absolute rounding error in bfloat16?
Transcribed Image Text:4. The bfloat 16 "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? (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 00000110 (c) Given that the largest exponent actually used for numbers is 11111110, what is the largest number that can be expressed as a bfloat 16? 0100010 (d) Supposing that numbers are truncated (rounded down), what is the maximum absolute rounding error in bfloat16?
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