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This chapter is from the book

This chapter is from the book

Conversion Between Binary, Hex, and Decimal

The following sections provide an introduction to converting between binary, hex, and decimal. Again, there is more than one mathematical approach to finding the correct answer, but the method shown is simple and reliable.

Decimal to Hexadecimal Conversions

The easiest way to get from decimal to hexadecimal and back is to go through binary. Take the example we used earlier in which we converted 176 decimal to binary:

176 = 10110000

Given that a single hex character represents 4 binary bits, all we need to do is to break the 8-bit string 10110000 into two 4-bit strings like this:



Now, simply match the 4-bit strings to their hex equivalent:

1011 = B

0000 = 0

The answer is simply 10110000 = 0xB0.

The "0x" in front of the answer is an expression that means "the following is in hex." This is needed because if the hex value was 27, we could not distinguish it from 27 decimal.

Hexadecimal to Decimal Conversions

The reverse of the procedure is easier than it seems, too. Given a hex value of 0xC4, all we need to do is to first convert to binary, and then to decimal.

To convert to binary, take the two hex characters and find their binary value:

C = 1100

0100 = 4

Now, make the two 4-bit strings into one 8–bit string:


Finally, add the bit values of the columns where you have a 1:

128 + 64 + 4 = 196

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