How to Count in Binary
Learn what binary means., Add one by changing the last 0 into a 1., Write another digit if all the numbers are one., Use these rules to count to five., Count to six., Count to ten., Notice when new digits get added., Practice with higher numbers.
Step-by-Step Guide
-
Step 1: Learn what binary means.
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. -
Step 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. , 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. 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. , 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 , 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 , 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 , 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). , 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.) -
Step 3: Write another digit if all the numbers are one.
-
Step 4: Use these rules to count to five.
-
Step 5: Count to six.
-
Step 6: Count to ten.
-
Step 7: Notice when new digits get added.
-
Step 8: Practice with higher numbers.
Detailed Guide
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.
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. , 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. 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. , 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 , 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 , 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 , 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). , 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.)
About the Author
Joyce Edwards
Professional writer focused on creating easy-to-follow home improvement tutorials.
Rate This Guide
How helpful was this guide? Click to rate: