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The decimal equivalent of (101111.1101)2 is
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:
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?
1, 3, and 4
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.
Match List-l with List-ll and select the correct answer using the codes given below the lists:
The following two numbers are converted into desired bases x and y respectively.
The values of x and y are respectively
The binary number is converted into octal number as follows:
On converting the decimal number (7864)10 into hexadecimal number we obtain the result (EB8)16 as follows:
Thus, (7864)10 = (1EB8)16
If (100110) x (x)10 = (101010110)2, then the value of x will be equal to
From above multiplication, it is clear that,
The range of numbers that can be represented using 6-bits in signed binary number representation is
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.
A decimal number (22)10 may be represented by the following ways:
The binary equivalent of (22)10 = (10110)2 as follows:
∴ (22)10 = (10110)2
Thus, (10110)2 = (11101)gray
The 7-bit even parity Hamming code of the binary bits 0101 is
∴ The required 7-bit even parity Hamming code is ( 0 1 0 0 1 0 1).
If (2AC9)16 = (Z)7, then the value of Z is
Thus, (2AC9)16 - (10,953)10
Now, the decimal number is converted into the number of base 7 as follows:
Assertion (A): Digital circuits are often called switching circuits.
Reason (R): Each type of digital circuit obeys a certain set of logic rules.
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.