Question

Matlab uses IEEE double precision numbers: 64-bit floating point representation

1 bit : sign

11 bits: exponent

52 bits: mantissa.

Calculate largest number that can be stored accurately

Calculate smallest number (x>0) that can be stored accurately

Calculate the machine epsilon

Show all work step by step and explain calculations

Now calculate the largest number and smallest number for a 10 bit floating point (1 bit for the sign, 4 bits exponent and 5 bits mantissa)

Answer #1

Matlab uses IEEE double precision numbers: 64-bit floating point
representation
1 bit : sign
11 bits: exponent
52 bits: mantissa.
Calculate largest number (less than inf) that can be stored
accurately
Calculate smallest number (x>0) that can be stored
accurately
Calculate the machine epsilon
Show all work step by step and repeat for 10 bit floating point
(bit sign, 4 bits exponent and 5 bits mantissa)

Given a 12-bit IEEE floating point format with 5 exponent
bits:
Give the hexadecimal representation for the bit-pattern
representing −∞−∞.
Give the hexadecimal representation for the bit-patterns
representing +0 and -1.
Give the decimal value for the floating point number represented
by the bit-pattern 0xcb0.
Give the decimal value for largest finite positive number which
can be represented?
Give the decimal value for the non-zero negative floating point
number having the smallest magnitude.
What are the smallest and largest magnitudes...

Concern the following 16-bit floating point representation: The
first bit is the sign of the number (0 = +, 1 = -), the next nine
bits are the mantissa, the next bit is the sign of the exponent,
and the last five bits are the magnitude of the exponent. All
numbers are normalized, i.e. the first bit of the mantissa is one,
except for zero which is all zeros.
1. How many significant binary digits do numbers in this
representation...

Assuming a 5-bit IEEE (754 standard) floating-point format
where 1 bit is used for the sign, 3 bits for the exponent, and 1
bit for the fraction, write the formulas for the exponent E, the
significand M, the fraction f, and the value V for the quantities
that follow and also describe the bit representation. Please show
all steps to receive full credit.
The number 5.0
The largest odd integer that can be represented exactly
The reciprocal of the smallest...

Question 9.1 Half-precision Floating-point Format
Do some research and find out how real (floating point) numbers
are represented in Binary.
(a) (10 =6+4 marks) Devise your own 16-bit representation for
floating point numbers. Draw a diagram of your representation and
explain what the various bits are used for.
Explain in detail:
(i) How many bits are allocated to the mantissa and the
exponent, respectively?
(ii) What defines the range and the precision (or accuracy) of
the numbers stored in floating...

urgent:
Consider a 5-bit floating point representation based on the
IEEE floating point format with one sign bit, the next two bits of
the exponent (exponent bias is 1), and the last two bits of the
significand. Fill in the table below. For column M and Value, your
answer must be expressed as a fraction of the form x/4.
Bits
M
E
Value
0 01 00
0 01 01
0 01 10
0 01 11
0 10 00
1
4/4...

Using the IEEE single-precision floating point representation,
find the decimal number represented by the following 32-bit
numbers, each expressed as an 8-digit hex number. Express your
answer using decimal scientific notation.
(a) (C6500000)16 (b) (31200000)16

double x = 1000000.
1. Calculate the smallest positive number that can be added to
x that will not be lost in the
mantissa.
2. In general, what is the ratio of the large and smallest
double-precision floating point numbers that can be added together
without a loss of data?

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