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What is the decimal value for the binary number 1001.0010?1. 1252. 12.53. 90.1254. 9.125 |
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Answer» Correct Answer - Option 4 : 9.125 Concept : The binary number system with only two independent digits, 0 and 1, is a base-2 number system. All larger binary numbers are represented in terms of ‘0’ and ‘1’. The decimal number is equal to the sum of binary digits (Dn) times their power of 2 (2n) Decimal = --- + D2 × 22 + D1 × 21 + D0 × 20 In order to convert the binary fractions to decimal numbers, we use negative power of 2 to the right of the binary point. = D-1 2-1 + D-2 2-2 + --- Calculation: Given binary number is: 1001.0010 The decimal equivalent of the integer part will be: (Decimal)Integer = (1) × 23 + (0) × 22 + (0) × 21 + (1) × 20 = 8 + 1 = 9 The fractional part will be: (Decimal)Fractional = (0) × 2-1 + (0) × 2-2 + (1) × 2-3 + (0) × 2-4 = 2-3 = 0.125 ∴ The resultant decimal equivalent is: (1001.0010)2 = (9.125)10 |
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