Книга: Introduction to Microprocessors and Microcontrollers

Converting binary to hex

This is very easy. Four binary bits can have minimum and maximum values of 0000₂ up to 1111₂. Converting this into denary by putting in the column headers of: 8, 4, 2 and 1 results in a minimum value of 0 and a maximum value of 15₁₀. Doesn’t this fit into hex perfectly!

This means that any group of four bits can be translated directly into a single hex digit. Just put 8, 4, 2 and 1 over the group of bits and add up the values wherever a 1 appears in the binary group.

Example

Convert 100000010101011₂ to hex

Step 1 Starting from the right-hand end, chop the binary number into groups of four.

100/ 0000/ 1010/ 1011/

Step 2 Treat each group of four bits as a separate entity. The right-hand group is 1011 so this will convert to:

The total will then be 8 + 0 + 2 + 1 = 1110 or in hex, B. The right-hand side binary group can now be replaced by the hex value B.

Step 3 The second group can be treated in the same manner. The bits are 1010 and by comparing them with the 8, 4, 2, 1 header values this means the total value is (8?1)+(4?0)+(2?1)+(1?1) = 8 + 0 + 2 + 0 = 1010 or in hex, A.

We have now completed two of the groups.

Step 4 The next group consists of all zeros so we can go straight to an answer of zero. The result so far will be:

Step 5 The last group is incomplete so only the column headings of 4, 2, and 1 are used. In this case, the 4 is counted but the 2 and the 1 are ignored because of the zeros. This gives a final result of:

So, 100000010101011₂ = 40ABH.

Having chopped up the binary number into groups of four the process is the same regardless of the length of the number. Always remember to start chopping from the right-hand side.

Example

Convert the number 1100011111001₂ to hex

Split it into groups of four starting from the right-hand side

1/ 1000/ 1111/ 1001/

Add column headers of 8 4 2 1 to each group

Now just convert group values to hex as necessary. In this example only the second group 15, will need changing to F. Final result is 1100011111001₂=18F9H.

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