Question in image. Thank you for helping. IEEE 754 floating point numbers (single precision) use the following format (the numbers on thetop of the box indicate bit positions, the fields in the box indicate what the various bits mean).01230 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+-+-+-+- -+-+-+-+-+---+-+-+-+-+-+-+-+-+-++-+-+-+ISImantissa (23 bits)-+-+-+-+-+-+-+-+-+-+-+-+-+-+- -+-+-+-++-+-exponent I+-+-+-+-+-+-+-+-+-+-+-+-IThe encoding starts with a sign bit, followed by the biased exponent (8 bits), followed by themantissa (23 bits). For single-precision floating-point numbers, the exponents in the range of -126to +127 are biased by adding 127 to get a value in the range 1 to 254 (0 and 255 have specialmeanings).b) What is the decimal fraction that is actually stored in the single precision floating point numberand what is the absolute error?

Answered: IEEE 754 floating point numbers (single…

Database System Concepts

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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
mantissa (23 bits)
-+-+-+-+-+-+-+-+-+-+-+-+-+-+- -+-+-+-+
+-+-
exponent I
+-+-+-+-+-+-+-+-+-+-+-+-
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).
b) What is the decimal fraction that is actually stored in the single precision floating point number
and what is the absolute error?

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Step 1

Introduction

The 32-bit single-precision floating-point format may represent a broad range of numerical values and requires 32 bits of computer memory. This format, sometimes known as FP32, is best suited for calculations that do not need an approximation.

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