This question was previously asked in

VSSC (ISRO) Technician B (Electronic Mechanic) Previous Year Paper (Held on 25 Sept 2016)

Option 4 : 9.125

Subject Test 1: Electrical Basics

3012

20 Questions
80 Marks
30 Mins

__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}**