Question

Show that in 2’s complement binary system, the highest significant position acts like a sign (not the same) as in the signed-magnitude binary system. Is this true for any radix-r number system? Justify your answer.

Answer #1

**It is NOT
true for any radix-r number system.**

For binary number system it is true that highest significant bit acts as sign bit for both signed magnitude representation and 2's complement representation, but it is no true for all. We can prove it by contradiction, in decimal representation signed magnitude form we dont use highest significant bit as sign bit, instead we use '+' / '-' as prefix of the number for signed magnitude representation, hence proved the above statement is not true.

The 8-bit signed binary 2's complement number equal to the
decimal number -73 is [a].

Perform the following operation in the Signed 2’s complement
system. Use eight bits for each number. Check your results by
converting the binary result back to decimal. Please show all the
steps, also please type steps and answer no picture upload from
written work please
Add +68 to -45

Find the 2's complement of the following decimal numbers (You
must convert the number to binary and the answer has to be in
binary with the same number of bits as the conversion)?
a. 20
b. 15
c. 2126
d. 266
e. 466
please explain how you did it!

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.

Sign extension means that any given signed number can be
represented with more bits by simply repeating the sign bit. For
example, 0005 = +5 and 00005 = +5. This holds true for negative
numbers as well. For example, 1011 = -5 and 11011 = -5. Also,
11111011 = -5. Using finite summation notation, prove that sign
extension can be applied to any 2's complement binary integer, B,
with b number of bits

Consider the number below, which is stored inside a computer
which uses 16-bit 2’s complement base 2 representation.
1101011001110101
(a) Is this number negative? Why, or why not?
(b) Show the resulting value (“bit pattern”) after
apply the 2’s complement negation operation to the given value. Is
the resulting 2’s complement value (“bit pattern”) a negative
number? Explain your answer.

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S′ = −aSI,
I′= aSI−bI,
R′ = bI.
a) The threshold level for S—below which the number of infected
will only decline—can be expressed in terms of the transmission
coefficient a and the recovery coefficient b. What is that
expression?
b) Consider two illnesses with the same transmission coefficient
a; assume they differ only in the length of time someone stays ill.
Which one has the lower threshold level for...

Adder
Start out by picking 2 positive six bit binary numbers that are
less than 3210, written in 2's complement notation. The
eventual goal is to add these two numbers.
1) Look at the LSB bit of the numbers, and using logic gates
(NANDs, NORs, etc.) design a circuit that correctly gives the right
output for any possible combination of bits in the LSB place.
2) Now look at the next column to the left (next to LSB). In
this...

A newly installed automatic gate system was being tested to see
if the number of failures in 1,000 entry attempts was the same as
the number of failures in 1,000 exit attempts. A random sample of
eight delivery trucks was selected for data collection. Do these
sample results show that there is a significant difference between
entry and exit gate failures? Use α = 0.01.
Truck 1
Truck 2
Truck 3
Truck 4
Truck 5
Truck 6
Truck 7
Truck...

A newly installed automatic gate system was being tested to see
if the number of failures in 1,000 entry attempts was the same as
the number of failures in 1,000 exit attempts. A random sample of
eight delivery trucks was selected for data collection. Do these
sample results show that there is a significant difference between
entry and exit gate failures? Use α = 0.05.
Truck 1
Truck 2
Truck 3
Truck 4
Truck 5
Truck 6
Truck 7
Truck...

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