Question 7 - Sample Paper 1 by Teachoo - Teachoo Sample Paper

In the binary number system, each digit can represent 2 possible values, 0 or 1. What is the binary equivalent of the decimal number 25? 

a. 11001 

b. 10110 

c. 10011 

d. 11100

Answer:

Answer by student

a. 11001

Detailed answer by teachoo

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To convert a decimal number to a binary number, we need to divide the decimal number by 2 repeatedly and write down the remainders in reverse order. For example, to convert 25 to binary, we can do the following:

• 25 / 2 = 12, remainder = 1 
• 12 / 2 = 6, remainder = 0 
• 6 / 2 = 3, remainder = 0 
• 3 / 2 = 1, remainder = 1 
• 1 / 2 = 0, remainder = 1

The remainders are 1, 0, 0, 1, and 1. If we write them in reverse order, we get 11001 , which is the binary equivalent of 25.

Let’s check the options and see why they are correct or incorrect:

a. 11001

This is the binary equivalent of 25.

b. 10110

This is not the binary equivalent of 25, because if we convert it back to decimal, we get:

10110 = (1 * 2^4) + (0 * 2^3) + (1 * 2^2) + (1 * 2^1) + (0 * 2^0) = (16) + (0) + (4) + (2) + (0) = 22

c. 10011

This is not the binary equivalent of 25 , because if we convert it back to decimal, we get:

10011 = (1 * 2^4) + (0 * 2^3) + (0 * 2^2) + (1 * 2^1) + (1 * 2^0) = (16) + (0) + (0) + (2) + (1) = 19

d. 11100

This is not the binary equivalent of 25 , because if we convert it back to decimal, we get:

11100 = (1 * 2^4) + (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (0 * 2^0) = (16) + (8) + (4) + (0) + (0) = 28

So, the correct answer is a. 11001.

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