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QUESTION: 1

The decimal equivalent of (101111**.**1101)_{2} is

Solution:

A binary number can be converted into decimal number by multiplying the binary numbers 1 or 0 by their weight and adding the product. Conversion of 101111 is done as follows:

QUESTION: 2

Consider the following statements associated with data representation by 1’s and 2‘s complements:

1. The 2’s complement system requires only one arithmetic operation.

2. The 1 ’s complement system requires two arithmetic operations.

3. The 1 's complement is often used in logical manipulations for inversion operation.

4. The 2 ’s complement is used only for arithmetic applications.

Which of the statements given above are correct?

Solution:

QUESTION: 3

Match List-l with List-ll and select the correct answer using the codes given below the lists:

Solution:

- “Hamming Code” provides a mathematical way to add one or more parity bits to a data character in order to detect and correct errors.
- “Gray code” is also called a “unit-distance code” because here two adjacent code numbers differ by only one bit.
- “Excess-3 code" is called a “reflective code” because here the code for 9 is the complement of the code for 0, 8 for 1,7 for 2, 6 for 3, and 5 for 4.
- “BCD code” is as “weighted code” or “8421 code” because it uses the binary number system to specify the decimal number 0 to 9.

QUESTION: 4

The following two numbers are converted into desired bases x and y respectively.

The values of x and y are respectively

Solution:

The binary number is converted into octal number as follows:

Thus,

(7-FD6)_{16}= (7.7726)_{8}

On converting the decimal number (7864)_{10} into hexadecimal number we obtain the result (EB8)_{16} as follows:

Thus, (7864)_{10} = (1EB8)_{16}

QUESTION: 5

If (100110) x (x)_{10} = (101010110)_{2}, then the value of x will be equal to

Solution:

From above multiplication, it is clear that,

QUESTION: 6

The range of numbers that can be represented using 6-bits in signed binary number representation is

Solution:

In signed binary number representation, the range of number that can be represented by an n -bit number is

For n = 6, the range is -31 to + 31.

QUESTION: 7

A decimal number (22)_{10} may be represented by the following ways:

Solution:

The binary equivalent of (22)_{10} = (10110)_{2} as follows:

∴ (22)_{10} = (10110)_{2}

- The GRAY code of (10110)
_{2}is obtained as follows:

Thus, (10110)_{2} = (11101)_{gray}

- The octal equivalent of (22)
_{10}= (26)_{8}obtained as follows:

- The hexadecimal equivalent of (22)
_{10}obtained as follows:

QUESTION: 8

The 7-bit even parity Hamming code of the binary bits 0101 is

Solution:

Given,

∴ The required 7-bit even parity Hamming code is ( 0 1 0 0 1 0 1).

QUESTION: 9

If (2AC9)_{16} = (Z)_{7}, then the value of Z is

Solution:

Thus, (2AC9)_{16} - (10,953)_{10}

Now, the decimal number is converted into the number of base 7 as follows:

Thus

QUESTION: 10

Assertion (A): Digital circuits are often called switching circuits.

Reason (R): Each type of digital circuit obeys a certain set of logic rules.

Solution:

Digital circuits are often called switching circuits, because the voltages in a digital circuit are assumed to be switching from one value to another instantaneously, that is, the transition time is assumed to be zero.

Reason is also a correct statement because digital circuit is a logic circuit, because each type of digital circuit obeys a certain set of logic rules. Hence, both assertion and reason are true but reason is not the correct explanation of assertion.

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