Question

Show each step to find the 8-bit representation of
**-33 _{10}**

Answer #1

- There are total of 3 methods (1)signed magnitude (2) signed
1
^{'s}complement (3) signed 2's complement.

Although nowadays computers used signed 2's complement to store negative numbers. so using this I solved.

Translate the base 10 value -45 into 8-bit two's complement
representation.

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)

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 two’s complement representation for the following
numbers, assuming they are represented as a 16-bit number. Write
the value in both binary and hexadecimal for full credit.
a. -72
b. 1314
c. 594
d. -1194

What is the 16-bit binary representation (in hexadecimal using
lower-case letters, e.g., 0x39ab) of -13 1/4 (base 10) when
represented as an IEEE 16-bit ﬂoating-point number? The IEEE 16-bit
ﬂoating-point representation uses formulae consistent with those
for the 32bit single-precision representation, except for using 5
bits for the exponent (instead of 8 in the case of the 32-bit
representation) and a bias of 15.

Assuming nine-bit 2’s complement representation, convert the
decimal number -137 to binary, show the effect of
the ROL operation on it with initial carry C=1,
show the status bits and then convert the result back to decimal.
Repeat with the ASR operation. Write the
RTL specification of both operations shown
here.

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...

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...

Using the 32-bit binary representation for floating point
numbers, represent the
number 10111001100112 as a 32 bit floating point
number.

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