Find the hexadecimal expansion

Question

Find the hexadecimal expansion of (177130)₁₀

Summary

Here in the given question, we have decimal expansion and we have to convert it into hexadecimal expression. We can convert the number or expansion from one type to another. So basically there are four types of number systems. Which first is the Binary number which consists of only two numbers i.e. 1 and 0. Next is Octal which consists of numbers from 0-7. In every number system, 0 is included and counted.

Next is the decimal number system which consists of 10 numbers as we already know decimal means 10. the last and final number system is the Hexadecimal number system. So this number system includes total numbers 16. But as it includes 0 the range of the hexadecimal is from 0-15. In which first 0-9 are represented by numbers and the rest of them are represented by alphabets.

Explanation

There are 4 standard number systems based on the radix.

• •  Binary number system (radix = 2)
  •  Octal number system (radix = 8)
  •  Decimal number system (radix = 10)
  • Hexadecimal number system (radix = 16)

Here in the given question, we are given the number with the decimal expansion i.e. 10. We have to convert the given number into the hexadecimal expansion. It is possible to convert one expansion to another.

So now the question is how the conversion is possible?

Each time we will divide the number by 16. After the number is divided it will give us the remainder. Then divide the remainder with the 16. We will divide this until the remainder will be less than 16 i.e. radix. Then the remainder in reverse order gives us the hexadecimal number.

After the 0 remaining numbers until 16 are represented alphabetically. So this will look like

10 = A
11 = B
12 = C
13 = D
14 = E
15 = F

So the final answer is (21131410)

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