Question

19. Use the 64-bit long real format to find the
decimal equivalent of the following floating-point machine

numbers.

a.

0100000010101001001100000000000000000000000000000000000000000000

b.

1100000010101001001100000000000000000000000000000000000000000000

c.

0011111111110101001100000000000000000000000000000000000000000000

d.

0011111111110101001100000000000000000000000000000000000000000001

Answer #1

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...

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)

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)

Perform the following using 10-bit floating point notation
having the format SEEEMMMMMM:
a. Decode 1101110110 to decimal integer and/or fraction.
b. Decode 0001100000 to decimal integer and/or fraction.
c. Encode: -5/32
d. Encode: +6 and 5/8
If someone could send the answer with explanations please do. It
will be greatly appreciated.

Convert the number 425.6 to the IEEE-754 32-bit floating point
format.
Don't use cheet

2 Convert each of the following octal numbers to 10-bit binary,
hexadecimal, and decimal. Show your work.
(a) 368
(b) 7568
3 Convert the following binary values into Decimal, Octal and
hexadecimal. Show your work.
(a) 111010101011112
(b) 1010111011001102
(c) 1011101010001112
(d) 1111101011102
4 Convert the following hexadecimal numbers to 16-bit binary and
decimal numbers. Show your work.
(a) FE9816
(b) FCAD16
(c) B00C16
(d) FEDF16
5 Perform the addition on the following unsigned binary numbers.
Indicate whether or not...

How do you convert a decimal like 4.9219 into binary? (assuming
32-bit IEEE 754 floating point format)

Find the internal representation of the following decimal number
in the Single Precision Floating Point format of the value:
-17.6
Non-terminating fractions should be carried out 6 places. You
will show the different steps involved in this transformation by
filling out the fields below.
The value 17 in binary is ___ 2 (no leading or
trailing zeroes).
The value .6 in binary is ____ 2 (complete to 6
places)
Normalized fraction: 1.____ 2 x 2Exponent.
Exponent=_____.
Biased Exponent in Binary:...

Using 14 bit fixed floating point with an implied 1 (normalized)
and excess-16 standards, give the decimal value of the numbers
below.
a) 00101111000100 b) 01010111000100 c) 00101010001100 d)
01011010001100

For each of the following, assume that we are using a 32-bit
system with single-precision (32-bit) floating point numbers
(floats) in IEEE format, double-precision (64-bit) doubles in IEEE
format, and 32-bit integers. Which of the following evaluate to
true for all argument values? (Circle each that is always
true).
char c = ..
int x = ..
short y = ..
float f = ..
double d = ..
c == (char)(float) c
y == (short)(int) y
f == (float)(double)...

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