Assume a 10-bit floating point representation format where the Exponent Field has 4 bits
Assume a 10-bit floating point representation format where the Exponent Field has 4 bits and the Fraction Field has 6 bits and the sign bit field uses 1 bit
S Exponent Field: 4 bits Fraction Fleld: 5 bits
a) What is the representation of -8.80158 × 10-2 in this Format - assume bias =2M-1-1=24-1-1=7 (where N= number of exponent field bits) for normalized representation 1 -bias =-6 : for denormalized representation
b) What is the range of representation for positive normalized numbers?
c) What is the range of representation for positive denormalized numbers? (assume value of exponent =1-bias)
d) What 10-bit pattern represents the number -0.125=-1 / 8?
e) What base-10 integer or fraction does the above 10 bit floating point representation of 0101001001 equal to?
Homework Answers
Add Answer to:
Assume a 10-bit floating point representation format where the Exponent Field has 4 bits
Consider a 9-bit floating-point representation based on the IEEE floating-point format, with one sign bit, four...
Consider a 9-bit floating-point representation based on the IEEE floating-point format, with one sign bit, four exponent bits (k = 4), and four fraction bits (n = 4). The exponent bias is 24-1-1-7. The table that follows enumerates some of the values for this 9-bit floating-point representation. Fill in the blank table entries using the following directions: e : The value represented by considering the exponent field to be an unsigned integer (as a decimal value) E: The value of...
Assume the following representation for a floating point number 1 sign bit
Assume the following representation for a floating point number 1 sign bit, 4 bits exponent, 5 bits for the significand, and a bias of 7 for the exponent (there is no implied 1 as in IEEE). a) What is the largest number (in binary) that can be stored? Estimate it in decimal. b) What is the smallest positive number( closest to 0 ) that can be stored in binary? Estimate it in decimal.c) Describe the steps for adding two floating point numbers. d)...
If we use the IEEE standard floating-point single-precision representation (1 sign bit, 8 bit exponent bits...
If we use the IEEE standard floating-point single-precision representation (1 sign bit, 8 bit exponent bits using excess-127 representation, 23 significand bits with implied bit), then which of the following hexadecimal number is equal to the decimal value 3.875? C0780000 40007800 Oo 40780000 40A80010 The binary string 01001001110000 is a floating-point number expressed using a simplified 14-bit floating-point representation format (1 sign bit, 5 exponent bits using excess-15 representation, and 8 significand bits with no implied bit). What is its...
1. Assume we are using the simple model for floating-point representation as given in this book...
1. Assume we are using the simple model for floating-point representation as given in this book (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits, and a single sign bit for the number): a) Show how the computer would represent the numbers 100.0 and 0.25 using this floating-point format. b) Show how the computer would add the two floating-point numbers in part a by changing one of...
Inspired of the IEEE 754 standard, a floating point format that is only 10 bits wide is defined f...
Inspired of the IEEE 754 standard, a floating point format that is only 10 bits wide is defined for a special computer. The leftmost bit is still the sign bit, the exponent is 5 bits wide and has a bias of 15, and the fractions is 4 bits long. A hidden 1 is assumed for the normal number, but not for the denormalized number. c) Construct a case to show that floating point addition is not associative
Use a 10-‐bit model for floating point numbers, where one bit is used for the sign...
Use a 10-‐bit model for floating point numbers, where one bit is used for the sign bit, 4 bits are used for the exponent with a bias of 7, and 5 bits are used for the fraction. What is the smallest and largest positive normal value that can be represented?
(15 pt) A real number is represented by the IEEE floating format in 4-bit exponent and...
(15 pt) A real number is represented by the IEEE floating format in 4-bit exponent and 6-bit fraction (ignore the sign bit). 9. What is the floating point representation of the number 53/11 in the format ? a. Exponent Fraction b. What are values of the following floating-point numbers in binary scientific notations (e.g. 1.10*29 ? 0000 000001 0101 010101
A certain microcomputer uses a binary floating-point format with 4 bits for the exponent contains 4...
A certain microcomputer uses a binary floating-point format with 4 bits for the exponent contains 4 bits. The arithmetic e and 1 bit for the sign sigma. The normalized mantissa uses rounding. (a) Find the machine epsilon, i.e., the distance between 1 and the next larger floating- point number. (b) Let x = (7.125)_10. Find its floating-point approximation A(x). Give A(x) in decimal. (c) What is the relative error in A(x)
I would like a step by step explanation as to how the 7-bit floating point representations from Format A were converted...
I would like a step by step explanation as to how the 7-bit floating point representations from Format A were converted to Format B. Thanks. Consider the following two 7-bit floating point representations based on the IEEE floating point format. Neither has a sign bit - they can only represent non-negative numbers. i). Format A. There are k=3 exponent bits. The exponent bias is 3. There are n=4 fraction bits. ii). Format B. There are k=4 exponent bits. The exponent...
What's the decimal value of the following 8 bit floating point number? Suppose k=4 exponent bits,...
What's the decimal value of the following 8 bit floating point number? Suppose k=4 exponent bits, n=3 fraction bits, and the bias is 7 00111001
Consider a 9-bit floating-point representation based on the IEEE floating-point format, with one sign bit, four exponent bits (k = 4), and four fraction bits (n = 4). The exponent bias is 24-1-1-7. The table that follows enumerates some of the values for this 9-bit floating-point representation. Fill in the blank table entries using the following directions: e : The value represented by considering the exponent field to be an unsigned integer (as a decimal value) E: The value of...
If we use the IEEE standard floating-point single-precision representation (1 sign bit, 8 bit exponent bits using excess-127 representation, 23 significand bits with implied bit), then which of the following hexadecimal number is equal to the decimal value 3.875? C0780000 40007800 Oo 40780000 40A80010 The binary string 01001001110000 is a floating-point number expressed using a simplified 14-bit floating-point representation format (1 sign bit, 5 exponent bits using excess-15 representation, and 8 significand bits with no implied bit). What is its...
1. Assume we are using the simple model for floating-point representation as given in this book (the representation uses a 14-bit format, 5 bits for the exponent with a bias of 15, a normalized mantissa of 8 bits, and a single sign bit for the number): a) Show how the computer would represent the numbers 100.0 and 0.25 using this floating-point format. b) Show how the computer would add the two floating-point numbers in part a by changing one of...
(15 pt) A real number is represented by the IEEE floating format in 4-bit exponent and 6-bit fraction (ignore the sign bit). 9. What is the floating point representation of the number 53/11 in the format ? a. Exponent Fraction b. What are values of the following floating-point numbers in binary scientific notations (e.g. 1.10*29 ? 0000 000001 0101 010101
A certain microcomputer uses a binary floating-point format with 4 bits for the exponent contains 4 bits. The arithmetic e and 1 bit for the sign sigma. The normalized mantissa uses rounding. (a) Find the machine epsilon, i.e., the distance between 1 and the next larger floating- point number. (b) Let x = (7.125)_10. Find its floating-point approximation A(x). Give A(x) in decimal. (c) What is the relative error in A(x)
Most questions answered within 3 hours.
-
Consider the natural join of the relation R(A,B) and S(A,C) on
attribute A. Neither relations have...
asked 17 minutes ago -
You are a network planner tasked with developing an IP structure
for the following networks. The...
asked 1 hour ago -
Christmas Express makes wreaths in batch sizes of 30. The
cutting & assembly process takes 4...
asked 1 hour ago -
Suppose a brewery has a filling machine that fills 12-ounce
bottles of beer. It is known...
asked 2 hours ago -
For this problem, carry at least four digits after the decimal
in your calculations. Answers may...
asked 5 hours ago -
Ask a user for three positive integer numbers. Use an input
validation loop to make sure...
asked 5 hours ago -
The most primitive form of data from data analysis perspective
is a. nominal scale b. ordinal...
asked 6 hours ago -
The number of vacancies in some hypothetical metal increases by
a factor of 5 when the...
asked 6 hours ago -
The fiduciary duty that is predicated on the concept that a
board of directors and officers...
asked 6 hours ago -
Sustainable Growth Rate Last year Umbrellas Unlimited
Corporation had an ROE of 17.3% and a dividend...
asked 6 hours ago -
Write a MATLAB program to do the following:
Receive 5 input values and store them into...
asked 6 hours ago -
Which one of the following aqueous solutions would you expect to
have the largest conductance: (a)...
asked 6 hours ago