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In a binary number system, what is the decimal equivalent of 1011?
9
11
13
15
11
To convert a binary number to decimal, multiply each digit by 2 raised to the power of its position, starting from the right (0). For 1011, the calculation is (12┬│) + (02┬▓) + (12┬╣) + (12тБ░) = 8 + 0 + 2 + 1, which equals 11.
To convert a binary number to decimal, multiply each digit by 2 raised to the power of its position, starting from the right (0). For 1011, the calculation is (12┬│) + (02┬▓) + (12┬╣) + (12тБ░) = 8 + 0 + 2 + 1, which equals 11.
The binary number system uses base-2 and forms the foundation of modern digital computing, which relies on the logic gates developed by Claude Shannon in 1937, a core component of the Computer Hardware syllabus in RRB exams.
Binary uses only two digits: 0 and 1, known as bits.
The position values in binary represent powers of 2 (1, 2, 4, 8, 16, etc.).
Decimal to binary conversion involves repeated division by 2 and tracking remainders.
The rightmost digit is the Least Significant Bit (LSB) representing 2тБ░.
The leftmost digit in this example is the Most Significant Bit (MSB) representing 2┬│.
Option A (9) is 1001 in binary; Option C (13) is 1101 in binary; Option D (15) is 1111 in binary.
Modern computers use the binary system because electronic switches (transistors) are most reliably operated in two states: on (1) or off (0).
B is correct тАФ The binary sequence 1011 equates to 11 in the decimal system based on the positional power-of-two rule.
In RRB exams, binary-to-decimal conversion often appears alongside questions on Boolean Algebra and basic logic gates (AND, OR, NOT), which share the same binary logic foundations.