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IEEE 754 floating point numbers (single precision) use the following format (the numbers on the top of the box indicate bit positions, the fields in the box indicate what the various bits mean). 0 1 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 890123 +-+-+-+-+-+-+-+-- -+-+-+-+-+-+-+-+-+-+-+-+ mantissa (23 bits) -+-+-+-+ ISI exponent +-+-+-+-+-+- ト-+-- | +-+ -+-+-+-+-+-+ ト-+-+-+ I The encoding starts with a sign bit, followed by the biased exponent (8 bits), followed by the mantissa (23 bits). For single-precision floating-point numbers, the exponents in the range of -126 to +127 are biased by adding 127 to get a value in the range 1 to 254 (0 and 255 have special meanings). a) The standard acceleration of gravity is roughly 9.80665 meters per square seeconds. Explain step by step (in your own words) how the decimal fraction 9.80665 is converted into a single precision floating point number.

IEEE 754 floating point numbers (single precision) use the following format (the numbers on the top of the box indicate bit positions, the fields in the box indicate what the various bits mean). 0 1 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 890123 +-+-+-+-+-+-+-+-- -+-+-+-+-+-+-+-+-+-+-+-+ mantissa (23 bits) -+-+-+-+ ISI exponent +-+-+-+-+-+- ト-+-- | +-+ -+-+-+-+-+-+ ト-+-+-+ I The encoding starts with a sign bit, followed by the biased exponent (8 bits), followed by the mantissa (23 bits). For single-precision floating-point numbers, the exponents in the range of -126 to +127 are biased by adding 127 to get a value in the range 1 to 254 (0 and 255 have special meanings). a) The standard acceleration of gravity is roughly 9.80665 meters per square seeconds. Explain step by step (in your own words) how the decimal fraction 9.80665 is converted into a single precision floating point number.

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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IEEE 754 floating point numbers (single precision) use the following format (the numbers on the top of the box indicate bit positions, the fields in the box indicate what the various bits mean). 0 1 2 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 +-+-+-+-+-+-+-+-+-+- +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ ISI ·+−+-+-+-+-+-+-+-+- -+-+- exponent I −+−+-+-+-+ mantissa (23 bits) 1 The encoding starts with a sign bit, followed by the biased exponent (8 bits), followed by the mantissa (23 bits). For single-precision floating-point numbers, the exponents in the range of -126 to +127 are biased by adding 127 to get a value in the range 1 to 254 (0 and 255 have special meanings). a) The standard acceleration of gravity is roughly 9.80665 meters per square seeconds. Explain step by step (in your own words) how the decimal fraction 9.80665 is converted into a single precision floating point number.
Transcribed Image Text:IEEE 754 floating point numbers (single precision) use the following format (the numbers on the top of the box indicate bit positions, the fields in the box indicate what the various bits mean). 0 1 2 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 +-+-+-+-+-+-+-+-+-+- +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+ ISI ·+−+-+-+-+-+-+-+-+- -+-+- exponent I −+−+-+-+-+ mantissa (23 bits) 1 The encoding starts with a sign bit, followed by the biased exponent (8 bits), followed by the mantissa (23 bits). For single-precision floating-point numbers, the exponents in the range of -126 to +127 are biased by adding 127 to get a value in the range 1 to 254 (0 and 255 have special meanings). a) The standard acceleration of gravity is roughly 9.80665 meters per square seeconds. Explain step by step (in your own words) how the decimal fraction 9.80665 is converted into a single precision floating point number.
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Here we need to convert -273.15 to single precision floating point number.

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