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?
Match Listl with Listll 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:
Thus,
(7FD6)_{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}
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 6bits 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 7bit even parity Hamming code of the binary bits 0101 is
Given,
∴ The required 7bit 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:
Thus
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.
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