How do you convert a decimal number to a binary number?

Answer 1

First, realize that instead of one's, ten's, hundred's, thousand's etc. places you find in decimal, a binary number has a one's, two's, four's, eight's, sixteen's etc. places.

Start at the one's place. If there is a one here start with one.

Move to the left, whenever there is a one, add the corresponding place value to your total until you've reached the leftmost digit.

Example:

Convert 1011011001 in binary to decimal:

=1(1)+0(2)+0(4)+1(8)+1(16)+0(32)+1(64)+1(128)+0(256)+1(512)=729

Notice the bolded digits are the same in the original from right to left.

The italicized numbers are the appropriate powers of 2.
Binary numbers start with a column with the value of 1 on the right side. The next column, to the left, has double the value (which is 2), the next left doubles again (which is 4), then 8, 16, 32, 64, 128 etc. The inclusion of a number 1 in a column means that the number should be included in the total. The inclusion of a zero in a column means that the number should not be counted. Using just this combination of 1s and 0s any number can be represented. For example...
1 = 1
2 = 10
3 = 11
4 = 100
10 = 1010
15 = 1111
65 = 1000001

Answer 2

Binary numbers start with a column with the value of 1 on the right side. The next column, to the left, has double the value (which is 2), the next left doubles again (which is 4), then 8, 16, 32, 64, 128 etc. The inclusion of a number 1 in a column means that the number should be included in the total. The inclusion of a zero in a column means that the number should not be counted. Using just this combination of 1s and 0s any number can be represented. For example...

1 = 1

2 = 10

3 = 11

4 = 100

10 = 1010

15 = 1111

65 = 1000001

To convert decimals to binary numbers, a value of 1 in a digit place represents that exponential value of 2. For a four-digit binary number, these represent values of 8, 4, 2, and 1. Larger numbers will include larger values of 2.

Converting decimals

To convert a decimal number to a binary number, repeatedly divide by 2, rounding down in each step, remembering the remainders, until the result is zero. Write down the remainders in reverse order, and you have the binary number.

Here is another easy way to do this. First make a table that represents x2 multiplier as shown. Then take number such as 194, look at the table and put a 1 under the largest number that fits into 194, which is 128. Then subtract that, so we now have 66 left, move down the line now and look at 64. This goes into 66 once so put a 1 in that column as well. Now we have only 2 left so none of the numbers in the list will work until the number 2, so put 0's in all but 2. After this the number is 0, so the rest will be zero. The binary representative for 194 is 11000010. The number 1567 is also shown for example.

(1024) (512) (256) (128) (64) (32) (16) (8) (4) (2) (1)

11000010 is the value (128+64+0+0+0+2+0 = 194)

11000011111 is the value (1024+512+0+0+0+0+16+8+4+2+1 = 1567)

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Binary to Decimal

To convert the numbers from binary to decimal you can simply use a calculator and starting at the right side of the binary number if the first digit is 1 then add 1 to your calculator. If it is zero don't add anything, move left to the next column, if there is a 1 in this column add 2 to your total on your calculator, if it is a zero don't add anything, continue doing this, doubling the value for each column and adding the number if there is a 1 and ignoring it if there is a zero. For example....

The binary number 1100, starting at the right has 0 in the 1 column, 0 in the 2 column, 1 in the 4 column and 1 in the 8 column, so you would ignore 1 and 2 and simply add 4 + 8, giving your a value of 12, which is correct.

Answer 3

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