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Binary to Decimal or Decimal
to Binary
In order to understand the process the best, it is better for
you to learn how to convert form binary first, but if you would rather
skip this and go to the Decimal to Binary section,
please go ahead.
Convert Binary to Decimal utilizes a simple algorithm. For
practice lets use 101101.
First, space your binary number out:
1 0 1
1 0 1
Next, starting from the right, assign values to each binary number. Start
with 1 and multiply by two as you go to the right.
1 0
1 1 0
1
(32) (16) (8)
(4) (2) (1)
Now, you get to utilize the definition you learned for binary. For every
binary number that is '0' change its value to 0 (meaning OFF). Then, simply
add the values together.
1 0 1
1 0 1
(32) + (0) + (8) + (4) + (0) + (1) = 45
Therefore, the Binary value of 101101 is equal to 45.
Decimal to Binary or Binary
to Decimal
Converting Decimal to Binary is the same algorithm as before,
except reversed.
First, determine the amount of binary digits you need to have
for your number. For this example, we are going to use 74. Therefore, determine
the max value binary that you need for your number. Here is how you to
do it. Spread out your numbers as before and place the power of 2 under
it.
1 1 1
1 1 1 1
1
(128) (64) (32) (16) (8) (4) (2)
(1)
In observing this, you should realize you need only 7 binary digits. This
is because the eighth binary value is greater than the one we are converting.
Now, you need to determine which values need to be ON or OFF. To do this,
begin adding up your numbers from the left. After each addition, compare
your current number to the one you are trying to convert. If it is larger,
then assign the value you last added to zero.
1 0
0 1 0
1 0
(64) + (0) + (16) + (8) + (0) + (2) + (0) = 72
Therefore, 1001010 is equal to 72.
Have you had fun so far? I hope you now see why computers are so fascinating
to computer junkies like me. Any suggestions? Remember at any time you
feel that there is something that could be better please contact
me. Feel free to post the message on the message
board.
Continue the fun with Other Bases.
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