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ing point format: • There is a sign bit in the most significant bit. • The next 3 bits are the exponent. The exponent bias is 23-1 - 1 = 3. The last 3 bits are the fraction. • The representation encodes numbers of the form: V = (-1)³ ×M×2E, where M is the signif- icand and E is the biased exponent. The rules are like those in the IEEE standard (normalized, denormalized, representation of 0, infinity, and NAN). Fill in the table below. Here are the instructions for each field: Binary: The 7 bit binary representation. M: The value of the significand. This should be a number of the form x or x/y, where x is an integer, and y is an integral power of 2. Examples include 0, 3/4. E: The integer value of the exponent. Value: The numeric value represented. Note: you need not fill in entries marked with _". Minus zero Description Smallest denormalized (negative) Largest normalized (positive) One Positive infinity Binary 0 100 010 M Mantissa --- E Exponent Value -0.0 1.0 1.5 +x

ing point format: • There is a sign bit in the most significant bit. • The next 3 bits are the exponent. The exponent bias is 23-1 - 1 = 3. The last 3 bits are the fraction. • The representation encodes numbers of the form: V = (-1)³ ×M×2E, where M is the signif- icand and E is the biased exponent. The rules are like those in the IEEE standard (normalized, denormalized, representation of 0, infinity, and NAN). Fill in the table below. Here are the instructions for each field: Binary: The 7 bit binary representation. M: The value of the significand. This should be a number of the form x or x/y, where x is an integer, and y is an integral power of 2. Examples include 0, 3/4. E: The integer value of the exponent. Value: The numeric value represented. Note: you need not fill in entries marked with _". Minus zero Description Smallest denormalized (negative) Largest normalized (positive) One Positive infinity Binary 0 100 010 M Mantissa --- E Exponent Value -0.0 1.0 1.5 +x

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
Section: Chapter Questions
Problem 1PE
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please full file 6.png  this table after make table put right answers in it  here is refrence of my lecture note in 18.png this is not graded assigmnet this is paractice test question  

6. Consider the following 7-bit floating point representation based on the IEEE float- ing point format: There is a sign bit in the most significant bit. The next 3 bits are the exponent. The exponent bias is 23-1 -1 = 3. The last 3 bits are the fraction. The rules are like those in the IEEE standard (normalized, denormalized, representation of 0, infinity, and NAN). Fill in the table below. Here are the instructions for each field: Binary: The 7 bit binary representation. M: The value of the significand. This should be a number of the form x or x/y, where x is an integer, and y is an integral power of 2. Examples include 0, 3/4 . E: The integer value of the exponent. Value: The numeric value represented. Note: you need not fill in entries marked with "---". --- The representation encodes numbers of the form: V = (-1)³ ×M×2E, where M is the signif- icand and E is the biased exponent. • Minus zero --- Description Smallest denormalized (negative) Largest normalized (positive) One Positive infinity Binary 0 100 010 M Mantissa E Exponent Value -0.0 1.0 1.5 +x
Transcribed Image Text:6. Consider the following 7-bit floating point representation based on the IEEE float- ing point format: There is a sign bit in the most significant bit. The next 3 bits are the exponent. The exponent bias is 23-1 -1 = 3. The last 3 bits are the fraction. The rules are like those in the IEEE standard (normalized, denormalized, representation of 0, infinity, and NAN). Fill in the table below. Here are the instructions for each field: Binary: The 7 bit binary representation. M: The value of the significand. This should be a number of the form x or x/y, where x is an integer, and y is an integral power of 2. Examples include 0, 3/4 . E: The integer value of the exponent. Value: The numeric value represented. Note: you need not fill in entries marked with "---". --- The representation encodes numbers of the form: V = (-1)³ ×M×2E, where M is the signif- icand and E is the biased exponent. • Minus zero --- Description Smallest denormalized (negative) Largest normalized (positive) One Positive infinity Binary 0 100 010 M Mantissa E Exponent Value -0.0 1.0 1.5 +x
Dynamic Range (Positive Only) s exp frac Value Denormalized numbers Normalized numbers 0 0000 000 0 0000 001 0 0000 010 0 0000 110 0 0000 111 0 0001 000 0 0001 001 0 0110 110 0 0110 111 0 0111 000 0 0111 001 0 0111 010 0 1110 110 0 1110 111 0 1111 000 E -6 -6 -6 -6 -6 -6 -6 -1 -1 0 0 0 7 7 n/a 0 1/8*1/64 = 1/512 2/8*1/64 = 2/512 6/8*1/64 = 6/512 7/8*1/64 = 7/512 8/8*1/64 = 8/512 9/8*1/64 = 9/512 14/8*1/2 14/16 15/8*1/2 = 15/16 8/8*1 = 1 9/8*1 = 9/8 10/8*1 = 10/8 14/8*128 = 224 15/8*128 = 240 inf = Bryant and O'Hallaron, Computer Systems: A Programmer's Perspective, Third Edition v = (-1) M 2E n: E = Exp - Bias d: E = 1 Bias closest to zero largest denorm smallest norm closest to 1 below closest to 1 above largest norm 18
Transcribed Image Text:Dynamic Range (Positive Only) s exp frac Value Denormalized numbers Normalized numbers 0 0000 000 0 0000 001 0 0000 010 0 0000 110 0 0000 111 0 0001 000 0 0001 001 0 0110 110 0 0110 111 0 0111 000 0 0111 001 0 0111 010 0 1110 110 0 1110 111 0 1111 000 E -6 -6 -6 -6 -6 -6 -6 -1 -1 0 0 0 7 7 n/a 0 1/8*1/64 = 1/512 2/8*1/64 = 2/512 6/8*1/64 = 6/512 7/8*1/64 = 7/512 8/8*1/64 = 8/512 9/8*1/64 = 9/512 14/8*1/2 14/16 15/8*1/2 = 15/16 8/8*1 = 1 9/8*1 = 9/8 10/8*1 = 10/8 14/8*128 = 224 15/8*128 = 240 inf = Bryant and O'Hallaron, Computer Systems: A Programmer's Perspective, Third Edition v = (-1) M 2E n: E = Exp - Bias d: E = 1 Bias closest to zero largest denorm smallest norm closest to 1 below closest to 1 above largest norm 18
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