Humans
like to use decimal numbers, but we use binary numbers to represent what goes on
in digital circuits. Because of this, it is often necessary to convert decimal
numbers to binary and vice versa.

The
following procedure will convert a binary number to its decimal equivalent. This
example uses the binary number 10101101.

First, create a table that looks like
this.

Next, write the binary number in the
table

Finally, add up the numbers that have a 1
below them. The sum is the decimal equivalent of the binary number.

Therefore, 10101101 is 173 in decimal.

Converting Decimal to Binary

The
following procedure converts a decimal number to its binary equivalent. This
example uses the decimal number 182.

Find the highest number that will divide
into the decimal number you are converting and put a 1 in the cell below
that number. In this case, 128 is the highest number that will divide into
182. Subtract this number from the original decimal number.

Find the highest number that will divide
into the remainder and put a 1 in the cell below that number. In this
case, 32 is the highest number that will divide into 54. Subtract this
number from the original remainder.

Repeat this process until there is no
remainder.

Finally, fill in zeros between the ones.
The binary number in the table is the binary equivalent of the original
decimal number.

Binary Addition

There
are four rules for binary addition.

0
+0 0

Rule 1, 0 + 0 = 0

0
+1 1

Rule 2, 0 + 1
or 1 + 0 = 1

1 1
+1 0

Rule 3, 1 + 1 = 0 and carry
over to the next column to the left

1 1 1
+1 1

Rule 4, 1 + 1 + 1 (as with a carry from the
column to the right) = 1 and a carry over to the next column to the left

The
following two 8 bit numbers, when added together, show all the binary addition
rules in action.