Question

In the binary number 1110.101 the fractional part has the decimal value as 0.625 explain

Answer 1

Answer:

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Answer 2

$\bf\:(0.101)_2 = (0.625)_{10}$

Hence it has been proved that fractional part of binary number is equivalent to 0.625 in decimal number system.

Step-by-step explanation:

Given:

• A binary number 1110.101

To find:

• Prove that, the value of fractional part has decimal value as 0.625.

Solution:

Concept to be used:

Conversion of binary to decimal:

• Before decimal point: The binary number is multiplied by increasing positive powers of 2 from right to left,i.e. 2⁰,2¹,2²... and so on.
• After decimal point:The binary number is multiplied by increasing negative powers of 2 from left to right ,i.e. 2-¹,2-²... and so on.

Step 1:

Multiply the digits after decimal points with increasing negative powers of 2.

As digits of binary number are 101 after decimal point.

So,

$= (1 \times {2}^{ - 1}) +( 0 \times {2}^{ - 2} ) + (1 \times {2}^{ - 3} )$

or

$=\frac{1}{2} +0+ \frac{1}{8}$

Step 2:

Simplify the arithmetic expression.

$\frac{1}{2} = 0.5$

and

$\frac{1}{8} = 0.125$

So,

$= (0.5) + (0.125)$

or

$=0.625$

Thus,

$\bf\:(0.101)_2 = (0.625)_{10}$

Hence it has been proved that fractional part of binary number is equivalent to 0.625 in decimal number system.

Learn more:

1) convert 0.215 decimal to binary

https://brainly.in/question/14091766

2) 1. Convert the following Binary numbers to Decimal numbers

A . ( 10011 ) 2 = ( ? )10

B. (110101) 2 = ( ? ) 10

https://brainly.in/question/39681892

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