Binary is as Easy as 1 10 11

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Want to improve your nerd skills? Learn the counting system computers use for all their calculations. It looks strange at first, but you only need a few rules and a little practice to count in bin ary.

Reference table

Decimal	0	1	2	3	4	5	6	7	8	9	10
Binary	0	1	10	11	100	101	110	111	1000	1001	1010

1. 1

   Learn what binary means. ^[1] Our normal counting system is called decimal, or "base ten." We have ten different symbols for writing numbers, ranging from 0 to 9. Binary is a "base two" system, using only the symbols 0 and 1.^[2]

2. 2

   Add one by changing the last 0 into a 1. If a binary number ends in 0, you can count one higher by changing this to a 1. We can use this to count the first two numbers just as you would expect:

   • 0 = zero
   • 1 = one
   • For higher numbers, you can ignore the earlier digits of the number. 1010 + 1 = 1011.

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3. 3

   Write another digit if all the numbers are one. Now we have "1" for one, but we've already run out of symbols! In order to count to two, we need to write another digit. Add a "1" to the front of the number, and "reset" all the other digits to 0.^[3]

   • 0 = zero
   • 1 = one
   • 10 = two
   • This is the same rule we use in decimal when we run out of symbols (9 + 1 = 10). It just happens a lot more often in binary because we run out of symbols sooner.

4. 4

   Use these rules to count to five. These rules will get you as far as the number five. See if you can do it yourself, then check your work:

   • 0 = zero
   • 1 = one
   • 10 = two
   • 11 = three
   • 100 = four
   • 101 = five

5. 5

   Count to six. Now we need to solve five + one in decimal, or 101 + 1. The key here is to ignore the first digit. Just add the 1 + 1 at the end to get 10. (Remember, this is how you write "two".) Now restore the first digit and you get:

   • 110 = six

6. 6

   Count to ten. There are no new rules you need to learn. Try it yourself, then check your work with this list:

   • 110 = six
   • 111 = seven
   • 1000 = eight
   • 1001 = nine
   • 1010 = ten

7. 7

   Notice when new digits get added. Do you see that ten (1010) doesn't look like a "special" number in binary? Eight (1000) is much more important now, because it equals 2 x 2 x 2. Keep multiplying by two to find other important numbers like sixteen (10000) and thirty-two (100000).

8. 8

   Practice with higher numbers. Now you know everything you need to count in binary. If you're ever confused about what comes next, just work out what happens to the last digits. Here are a few examples to help you out:

   • twelve plus one = 1100 + 1 = 1101 (0 + 1 = 1, and the other digits stay the same.)
   • fifteen plus one = 1111 + 1 = 10000 = sixteen (We've run out of symbols, so we reset to 0 and write a 1 at the start.)
   • forty-five plus one = 101101 + 1 = 101110 = forty-six (We know 01 + 1 = 10, and the other digits stay the same.)

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1. 1

   Write down the value of each binary place. When you learned decimal counting, you learned about the "place values": the ones place, tens place, and so on.^[4] Since binary has two symbols, the place values multiply by two each time you move to the left:

   • 1 is the ones place
   • 10 is the twos place
   • 100 is the fours place
   • 1000 is the eights place

2. 2

   Multiply each digit by its place value. Start with the ones place on the far right, and multiply that digit (0 or 1) by one. On a separate line, move to the twos place, and multiply that digit by two. Repeat this pattern until you've multiplied each digit by its place value.^[5] Here's an example:

   • What is the binary number 10011 in decimal?
   • The rightmost digit is 1. This is in the ones place, so multiply by one: 1 x 1 = 1.
   • The next digit is also 1. Multiply this by two: 1 x 2 = 2.
   • The next digit is 0. Multiply this by four: 0 x 4 = 0.
   • The next digit is also 0. Multiply this by eight: 0 x 8 = 0.
   • The leftmost digit is 1. Multiply this by sixteen (eight times two): 1 x 16 = 16.

3. 3

   Add all the products together. Now you've converted each digit into its decimal value. To find the value of the full number, just add all the decimal values together. Here's the rest of your example:

   • 1 + 2 + 16 = 19.
   • The binary number 10011 is the same as the decimal number 19.

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Add New Question

• Question

  How many bits would I need if I wanted to have the ability to count up to 1000?

  

  Jordan Newberry

  Community Answer

  Ten bits. 1000 in binary is: 11 1110 1000 -- log₂(1000)≈9.966 bits. Of course, we can't use 9.966 bits, so we round up to the nearest integer: 10 bits.

• Question

  Can you summarize this topic?

  

  In binary notation, in the first column on the right (the "one" column), 0 means zero 1's, and 1 means one 1. In the next column to the left (the "two" column), 0 means zero 2's and 1 means one 2. In the next column (the "four" column), 0 means zero 4's, and 1 means one 4. The same pattern follows in each column. Moving to the left, the columns are "sixteen," "thirty-two," "sixty-four," and so on, each column being worth twice as much as the column to its right. For example, take the base-ten number 61: 61 consists of one 32 plus one 16 plus one 8 plus one 4 plus zero 2's plus one 1. So 61 is notated in binary as 111101 (pronounced "one one one one zero one").

• Question

  How do I convert 12 into binary?

  

  12 consists of one 8 plus one 4 plus zero 2's plus zero 1's, so the binary notation for 12 is 1100.

• Question

  How do I count to 6? I don't understand.

  

  6 consists of one 4 plus one 2. Therefore, you place a 1 in the four column and a 1 in the two column. So 6 in binary notation is 110.

• Question

  Does anything interesting happen when placing a zero to the right of a one?

  

  Nothing of general significance. A zero in any column simply means that that column is adding no value to the number being written.

• Question

  Why is 1 kilobyte equal to 1024 bytes instead of 1000 bytes?

  

  1 kilobyte is not equal to 1024 bytes, it's equal to 1000 bytes. While some applications (such as the Windows file system) still consider a kilobyte as 1024 bytes for binary calculations, the term kibibyte has been developed to refer to 1024 bytes so as to remove ambiguity.

• Question

  On ten fingers, how high can I count using binary?

  

  You can count up to the binary number 1111111111 (ten ones), which is 1,023 in decimal (base-10).

• Question

  What is binary number eight?

  

  Seeing as eight consists of eight without one, two or four added, it would be 00001000 in binary (the zeros at the start aren't needed, but can make it easier to differentiate between one thousand and binary eight).

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• You can also learn to count in binary on your fingers. Each finger is a digit, showing "1" if it's extended and "0" if it's curled down.^[6]

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Article Summary X

To count in binary, convert the last 0 in any number to 1 to add 1, and change any digits following the converted 1 back to 0. If all of the digits are already 1s, add a 1 to the beginning of the number and reset all of the other digits to 1. For instance, the number 1 is represented by 1, and the number 2 is written as 10. Following this, 3 is 11, 4 is 100, 5 is 101, 6 is 110, 7 is 111, 8 is 1000, and so on. To learn how to convert binary to decimal, read on!

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