Basics of Digital Electronics - 1 - GATE EE Free MCQ Test with solutions

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: 

1, 3, and 4

Explanation:

1. The 2's complement system requires only one arithmetic operation: This statement is correct. In the 2's complement system, both addition and subtraction can be performed with the same operation (addition). To subtract, we simply add the 2's complement of the number to be subtracted.

2. The 1's complement system requires two arithmetic operations: This statement is incorrect. The 1's complement system also requires only one arithmetic operation (addition) for both addition and subtraction. However, in this system, an end-around carry might be needed for the final result.

3. The 1's complement is often used in logical manipulations for inversion operation: This statement is correct. The 1's complement can be used to invert the bits of a binary number (changing 0s to 1s and vice versa). This operation is useful for logical operations like bitwise NOT.

4. The 2's complement is used only for arithmetic applications: This statement is correct. The 2's complement representation is primarily used for arithmetic operations, such as addition and subtraction, as it simplifies the operations and eliminates the need for separate circuits for these operations.

• “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.

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

From above multiplication, it is clear that, 

In a signed 6-bit binary number representation, the range of numbers is determined by the most significant bit (MSB), which is used as the sign bit.

Here's a breakdown of the range calculation:

1. Signed 6-bit binary numbers use the first bit (MSB) as the sign bit:

   • 0 indicates a positive number
   • 1 indicates a negative number

2. Positive numbers (MSB is 0):

   • The remaining 5 bits represent the magnitude.
   • The smallest positive number is 000000 (0 in decimal).
   • The largest positive number is 011111 (31 in decimal).

3. Negative numbers (MSB is 1):

   • The 2's complement method is used to represent negative numbers.
   • The smallest negative number is 100000 (-32 in decimal).
   • The largest negative number is 111111 (-1 in decimal).

Thus, the range of numbers that can be represented using 6-bit signed binary number representation is from -32 to 31.

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:

Given,

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

Thus, (2AC9)₁₆ - (10,953)₁₀

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

Thus

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.