Correct Answer - Option 4 : 41.125
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A number with base 2 is known as a Binary Number, and numbers with base 10 are known as Decimal Numbers in the Number System.
- The decimal numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and so on.
- Binary numbers, on the other hand, are used in digital systems and are represented by just two digits – 0 and 1.
Binary to Decimal Conversion:
Given:
Given binary number = (101001.0010)2
Calculation:
The decimal equivalent of the integer part will be:
(Decimal)Integer = (101001)2 = (1 × 25 + 0 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 1 × 20)10
⇒ (32 + 8 + 1)10
⇒ (41)10
The fractional part will be:
(Decimal)Fractional = (0.0010)2 = (0) × 2-1 + (0) × 2-2 + (1) × 2-3 + (0) × 2-4
= 2-3 = 0.125
So, the decimal equivalent of the binary number (101001.0010)2 is (41.125)10.
∴ The number at the place of the question mark will be 41.125.
