Want to improve your skills as a geek? Learn the calculation system that the computer uses for all of its calculations. It may seem strange at first, but you just need a few rules and practice to count in binary.
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 |
Step
Method 1 of 2: Studying Binary
Step 1. Learn about binary
The counting system we usually use is called decimal, or "base ten." There are ten different symbols for writing numbers, 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 to 1
If a binary number ends in 0, you can count one more by changing it to 1. We can use this to calculate the first two numbers as you would expect:
- 0 = zero
- 1 = one
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For larger numbers, ignore the first digits in the number. 101 0 + 1 = 101
Step 1..
Step 3. Write another number if all the numbers are 1
For the number one, the symbol is "1". However, after that, there was no other symbol! To count to two, another number must be written. Add "1" in front of the number, then "reset" all other numbers to 0.
- 0 = zero
- 1 = one
- 10 = two
- This is the same rule used for decimals if there are no more symbols after (9 + 1 = 10). However, this rule is more often intended for binary because there are only two symbols so they run out faster.
Step 4. Use this rule to count to five
This rule can be used up to five. See if you can do this yourself, then check your work:
- 0 = zero
- 1 = one
- 10 = two
- 11 = three
- 100 = four
- 101 = five
Step 5. Count to six
Now we have to solve for five + one in decimal, or 101 + 1 in binary. Here the key is to ignore the first number. Just add up 1 + 1 in the last number to get 10. (Remember, this way you write "two"). Now, return the first number and the result is:
110 = six
Step 6. Count to ten
There are no new rules to learn. Try it yourself, then check your work with the following list:
- 110 = six
- 111 = seven
- 1000 = eight
- 1001 = nine
- 1010 = ten
Step 7. Watch as new numbers are added
Did you notice that (1010) doesn't look like a "special" number in binary? Eight (1000) is now much more important because it is equivalent to 2 x 2 x 2. Keep multiplying by two to find other significant numbers like sixteen (10000) and thirty-two (100000).
Step 8. Practice with larger numbers
Now you know everything you need to calculate binary numbers. If you're confused about the next number, just work on the last digit. Here are some examples to help you:
- twelve plus one = 1100 + 1 = 1101 (0 + 1 = 1, and the other numbers remain the same).
- fifteen plus one = 1111 + 1 = 10000 = sixteen (Here we run out of number symbols again, so we reset it to zero and write 1 at the beginning).
- forty five plus one = 101101 + 1 = 101110 = forty six (We know 01 + 1 = 10, while the other digits remain the same).
Method 2 of 2: Converting from Binary to Decimal
Step 1. Write down the value of each binary place
When you learn to count decimals, you learn about "place values." Unit values, tens values, and so on are place values. Since binary has two symbols, the place value is doubled each time you move left:
- Step 1. is the unit place
- Step 1.0 is a double place
- Step 1.00 is the place of fours
- Step 1.000 is the eights place
Step 2. Multiply each number by its place value
Start with the units place on the far right, then multiply that number (0 or 1) by one. On a separate line, move to the second place, then multiply that number by two. Repeat this pattern until you finish multiplying each number by its place value. Here is one example:
- What is the binary number 10011 in decimal?
- The rightmost number is 1. This is the units place, so multiply by one: 1 x 1 = 1.
- The next number is 1. Multiply by two: 1 x 2 = 2.
- The next number is 0. Multiply by four: 0 x 4 = 0.
- The next number is 0. Multiply by eight: 0 x 8 = 0.
- The leftmost number is 1. Multiply by sixteen (eight times two): 1 x 16 = 16.
Step 3. Add up all the results
Now you have converted each number to its decimal value. To find the total number of numbers, just add up all the decimal values. Here's another example:
- 1 + 2 + 16 = 19.
- The binary number 10011 is the same as the decimal number 19.
