Convert AB6.4F Hex to Binary, Octal, Decimal

[noobie!]

Homework Statement

convert the hexadecimal number of AB6.4F to bas of 16 to its binary,octal,and decimal equivalent numbers..

Homework Equations

The Attempt at a Solution

i don't know what to refer,as what i know was 6.4 is an even number which could link up binary,octal but i have no idea where to begins with?...could you please give me some clue?

 

[heth]

What are all the possible digits that could appear in a hexadecimal number? (For example, the possible digits in a binary number are 1 and 0.)

If you're not sure, look it up in a book or online.

That should help you figure it out.

 

[thomate1]

I would first recognize that hexadecimal is a base 16 number system, meaning it uses 16 digits (0-9 and A-F) to represent numbers. To convert AB6.4F to binary, we can break it down into individual digits and convert each one to binary separately.

First, let's convert the letter A to its binary equivalent. In decimal, A is equivalent to 10. In binary, this is represented as 1010. Similarly, B is equivalent to 11 in decimal, which is represented as 1011 in binary. So, the first two digits of our binary number will be 101010.

Next, we need to convert the number 6. In decimal, 6 is equivalent to 110. Since hexadecimal is a base 16 system, we need to convert 6 to its base 16 equivalent. This is represented as 0110 in binary. So, our binary number now becomes 1010100110.

For the decimal point, we can simply leave it as is since it does not affect the binary conversion.

Finally, we need to convert the letter F to binary. In decimal, F is equivalent to 15. In binary, this is represented as 1111. So, our final binary number is 1010100110.1111.

To convert this binary number to octal, we can group the digits into groups of 3 starting from the right. So, our binary number becomes 101|010|011|0.111|1. In octal, these groups of 3 digits can be represented as 5|2|3|0.7|1. So, our final octal number is 5230.71.

To convert this binary number to decimal, we can use the place value system. Each digit in a binary number is multiplied by its corresponding power of 2, starting from 0 on the right. So, our decimal equivalent for 1010100110.1111 is (1*2^9) + (0*2^8) + (1*2^7) + (0*2^6) + (1*2^5) + (0*2^4) + (0*2^3) + (1*2^2) + (1*2^1) + (0*2^0) + (1*2^-1) + (