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) Describe the steps for multiplying two floating point numbers
Homework Answers
Add Answer to:
Assume the following representation for a floating point number 1 sign bit
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...
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 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 representationb) What is the range of representation for...
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?
Problem 5 (20 points) Consider a floating point number representation that is 16 bit wide. The...
Problem 5 (20 points) Consider a floating point number representation that is 16 bit wide. The leftmost bit is the sign bit, and the next 5 bits from the left make up an exponent (which has a bias of 15). The remainder 10 bits give the magnitude of the number. This representation assumes a hidden 1. Consider the number -1.3215 x 10-1 How doe its rine and acrac cmpare wit a he same number, this time b) How does 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...
Identify the floating point numbers corresponding to the following bit string IEEE 32 bit representation a)...
Identify the floating point numbers corresponding to the following bit string IEEE 32 bit representation a) 1 00000000 00000000000000000000000 Decimal or Binary number______________? b) 0 11111111 00000000000000000000000 Decimal or Binary number_______________? Would you please shoe me the steps please? Thank you!
Can anyone help me with this please
1. If the floating-point number storage on a certain system has a sign bit, a 4-bit exponent and a 5-bit significand: i) What is the largest positive and the smallest positive number that can be stored on this system if the storage is normalized? (Assume no bits are implied, there is no biasing, exponents use two's complement notation, and exponents of all zeros and all ones are allowed.) ii) What bias should be used in the exponent if we prefer...
. 2.1 a. Find the 16-bit 2’s complementary binary representation for the decimal number 1987. b. Find...
. 2.1 a. Find the 16-bit 2’s complementary binary representation for the decimal number 1987. b. Find the 16-bit 2’s complementary binary representation for the decimal number −1987. What are the 16-bit 1’s and 2’s complements of the following binary numbers? a. 10000 b. 100111100001001 Convert the decimal number 19557 to floating point. Use the format SEEMMMM. All digits are decimal. The exponent is stored excess-40 (not excess-50). The implied decimal point is at the beginning of the mantissa. The sign...
2.1 a. Find the 16-bit 2’s complementary binary representation for the decimal number 1987. b. Find...
2.1 a. Find the 16-bit 2’s complementary binary representation for the decimal number 1987. b. Find the 16-bit 2’s complementary binary representation for the decimal number −1987. What are the 16-bit 1’s and 2’s complements of the following binary numbers? c. 10000 d. 100111100001001 Convert the decimal number 19557 to floating point. Use the format SEEMMMM. All digits are decimal. The exponent is stored excess-40 (not excess-50). The implied decimal point is at the beginning of the mantissa. The sign...
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...
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...
Problem 5 (20 points) Consider a floating point number representation that is 16 bit wide. The leftmost bit is the sign bit, and the next 5 bits from the left make up an exponent (which has a bias of 15). The remainder 10 bits give the magnitude of the number. This representation assumes a hidden 1. Consider the number -1.3215 x 10-1 How doe its rine and acrac cmpare wit a he same number, this time b) How does 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...
Most questions answered within 3 hours.
-
284 mL of a 0.52 M potassium hydroxide solution is added to 467
mL of a...
asked 6 minutes ago -
exercise on VSEPR and molecular structrue.
octahedral
SeCl62-
TeCl62-
ClF62-
distorted
SeF62–
IF6–
asked 8 minutes ago -
Little’s Law: Val d’Costa is a world famous ski village in the
French Alps. Because of...
asked 1 hour ago -
Find the absolute error D for the calculation if A + B/C=D A=
9.4 +/- 0.4...
asked 1 hour ago -
New Air Heating and Cooling, manufactures furnaces and central
air units. The company pride itself on...
asked 1 hour ago -
A coach uses a new technique to train gymnasts. Seven
gymnasts were randomly selected and their...
asked 3 hours ago -
While rotating the tires on your car you notice a rock [mass =
0.1 Kg] stuck...
asked 5 hours ago -
Using MARS simulator, write MIPS programs according to
the following scenarios: Receive a positive integer number...
asked 7 hours ago -
An object in front of a concave mirror has a real image that is
11.5 cm...
asked 7 hours ago -
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 9 hours ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 9 hours ago -
In a study of the accuracy of fast food drive-through orders,
Restaurant A had 257 accurate...
asked 9 hours ago