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.