Question

Convert the following binary floating point number

100101.1001010101

using IEEE-756 single precision representation

Plz show work, thanks!

Answer #1

given binary floating point number : 100101.1001010101

i) spaces to move binary point so that it lands just after first
1 in the floating point number : 5

This gives us : 1.001011001010101

note: if we have to move left then it is positive else negative

ii) Add 127 to get exponent : 132

iii) convert exponent to binary : 10000100

iv) Adjust the Mantissa by removing the leading 1 from number we
got in step 1

001011001010101

v) **Result : 0 10000100 001011001010101**

first 0 is sign bit : 0 means positive. positive since we moved
left in step 1

next 8 bit is exponent

next 23 bit is mantissa

Convert the following floating-point number (stored using IEEE
floating-point standard 754) to a binary number in non-standard
form.
1100_0100_1001_1001_1000_0000_0000_0000

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

Find the single-precision IEEE 754 representation of 0.752.
Please show all work/steps.

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:...

1. Write the single-precision Representation for the following
decimal number. (-0.625) or -5/8. Final Results must be in HEX.
SHOW WORK PLEASE.
2. Given Hexadecimal 0x3F300000, convert it to decimal number if
it is a single precision floating point number. SHOW WORK
PLEASE.

If the IEEE Standard 754 representation of a floating point
number is given as 01101110110011010100000000000000, determine the
binary value represented by this 32-bit number

Represent the following decimal numbers using IEEE-754 floating
point representation. please show all work
i. -0.75
ii. 0
iii. - infinity
iv. 23
v. 10.25

Convert the following decimal numbers into IEEE single precision
format. Give your answer in hexadecimal. Show all
work
A) -15.5625
B) 10.9375

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)

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