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QUESTION: 1

(22)_{4} + (101)_{3} - (20)_{5} = (x)_{4} + (4)_{x-1} where x > 4 The value of x is:

Solution:

QUESTION: 2

If (28)_{x }in base x number system is equal to (37)_{y} in base y number system, the possible values of x and y are:

Solution:

QUESTION: 3

Suppose the largest n-bit binary number requires ‘d’ digits in decimal representation. Which of the following relation between ‘n’ and 'd’ is approximately correct?

Solution:

QUESTION: 4

Let A = 1111 1010 and B = 0000 1010 be two 8-bit 2’s complement numbers. Their product in 2’s complement is

Solution:

A = 11111010

Since MSB is 1 hence number is negative i.e. - (00000110)

= -(00000110)

A = - 6

B = 00001010,

There is number 2’s complement representation for positive number B = +10

A x B = 10 x (- 6)

= - 60

Binary representation of - 60 = 00111100

Now take 2’s complement = 11000100

QUESTION: 5

Which of the following 4-bit numbers equals its 1’s complement?

Solution:

Since in 1 ’s complete every bits get complemented so, no such number exist whose complement is same while in 2’s complement 8 and 0 are exist.

QUESTION: 6

If the decimal number is 3.248 x 10^{4} then its 32 bit equivalent floating number is

Solution:

Decimal number 3.248 x 10^{4}

So sign bit should be 0 since number is positive.

3.248 x 10^{4} = 32480

= 111111011100000_{2}

= 1.11111011100000 x 2^{14}

In normalized representation:

Biased = 14 + 127 = 14

= 10001101_{2}

So, number is

QUESTION: 7

A computer uses 8 digit mantissa and 2 digit exponent. If a = 0.052 and b = 28 E + 11, then b + a - b will

Solution:

a = 0.052 and b = 28 E + 1

So, b + a - b will b

a = 0.52 exponent

= -1

b = 28 E + 11 mantissa

= 0,28 exponent

= 13

b + a = 28000000000000 E - 1 + 0.52 E-1

= 280000000000.52 E - 1

With is equal to 28 E + 11

So, b - b = 0

QUESTION: 8

Consider the following floating point format;

S : Sign bit

E : Exponent

M : Mantissa

The value of floating point number in this system is, V = (-1 )^{s} x 2^{E-127} x 1.F

Then what is the corresponding decimal value if the floating point stored is: 3F800000

Solution:

QUESTION: 9

A single-precision floating point number contains the sequence of bits 100011111 00000000001 000000000000, Information is stored in the following left-to-right order, sign bit, exponent (bias 127) and mantissa. Which of the following representation in decimal is equivalent?

Solution:

QUESTION: 10

Sign extension is a step in

Solution:

Sign extension is the operation, in computer arithmetic, of increasing the number of bits of a binary number while preserving the number’s sign (positive/negative) and value.

QUESTION: 11

The decimal number 0.239 x 2^{13} has the following hexadecimal representation (without normalization and rounding off:

Solution:

The decimal number is 0.239 x 2^{13}

We have to find hexadecimal representation without normalization.

Biased exponent = 13 + 64 = 77

Representing 77 in binary (77)^{10} = (1001101)_{2}

Representing mantissa in binary

senting mantissa in binary (0.239)_{10} = 0.00111101000101

QUESTION: 12

The vales of x and y, if (x567)_{8} + (2yx5)_{8} = (71 yx)_{8} is

Solution:

(x 567)_{8}

(2yx5)_{8}

(71yx)8

x will be 4 and y will be 3.

QUESTION: 13

A decimal number has 25 digits. The numberof bits needed for its equivalent binary representation is, approximately,

Solution:

QUESTION: 14

The greatest negative number which can be stored in computer that has 8-bit work length and uses 2's complement arithmetic is

Solution:

Smallest number stored in 8 bit 2’s complement arithm etic is -2^{n-1}

=-2^{8- 1 }

= -128

QUESTION: 15

In the given network of AND

‘F' will be written as:

Solution:

F will represents x_{0} x_{1} x_{2} .... x_{n-1} x_{n}.

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