Question 23 - Sample Paper 1 by Teachoo - Teachoo Sample Paper

Convert the hexadecimal number given below to decimal number:

(3A5) ₁₆

Answer:

Answer by student

The decimal equivalent of the hexadecimal number (3A5) ₁₆ is 933 .

Detailed answer by teachoo

• The question asks us to convert a hexadecimal number to a decimal number. A hexadecimal number is a number that uses 16 symbols to represent digits, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. A decimal number is a number that uses 10 symbols to represent digits, namely 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
• To convert a hexadecimal number to a decimal number, we can use the following steps:
• Write the hexadecimal number in the form of a polynomial with powers of 16.  

For example, (3A5) ₁₆ can be written as (3 x 16 ² ) + (A x 16 ¹ ) + (5 x 16 ⁰ ).

• Convert each hexadecimal digit to its decimal equivalent. 

For example, A is equivalent to 10 in decimal. So, we can write (3 x 16 ² ) + (A x 16 ¹ ) + (5 x 16 ⁰ ) as (3 x 16 ² ) + (10 x 16 ¹ ) + (5 x 16 ⁰ ).

• Evaluate the polynomial by multiplying each term by its corresponding power of 16 and adding them up.  

For example, (3 x 16 ² ) + (10 x 16 ¹ ) + (5 x 16 ⁰ ) can be evaluated as (3 x 256) + (10 x 16) + (5 x 1), which is equal to 768 + 160 + 5 = 933 .

• Here is an example of how our calculation would look like:

(3A5) 16 = (3 x 16 ² ) + (A x 16 ¹ ) + (5 x 16 ⁰ )

               = (3 x 256) + (10 x 16) + (5 x 1)

               = 933

So, the decimal equivalent of the hexadecimal number (3A5) ₁₆ is 933.