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
