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Numerical · Q33

Q.Convert the binary number 101121011_2 to its decimal equivalent.

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Concept understanding — Decimal and Binary Number Systems

Decimal (base 10) uses ten digit symbols (00-99) with place values 100,101,102,…10^0,10^1,10^2,\ldots. Binary (base 2) uses only two symbols, called bits (0,10,1), with place values 20,21,22,…2^0,2^1,2^2,\ldots; a binary number's decimal value is the sum of each 11-bit's place value (e.g. 10112=8+0+2+1=11101011_2=8+0+2+1=11_{10}), and a decimal number is converted to binary by repeated division by 22, reading the remainders in reverse order. Binary is used in digital electronics because it maps d …

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