How to Read Binary

Trying to read a string of binary 1's and 0's can seem a daunting task. However, with a bit of logic we can figure out what they mean. Humans have adapted to use a base ten number system simply because we have ten fingers. Computers, on the other hand (no pun intended), have only two "fingers"--on and off or one and zero. Therefore, the base two number system has been created.

Steps

With Exponents

1. Find a binary number you want to convert. We'll use this as an example: 101010.
   
   
   


2. Multiply each binary digit by two to the power of its place number. Remember, binary is read from right to left. The rightmost place number being zero.
   
   
   


3. Add all the results together. Let's go from right to left.
   
   
   
   
   
   
   • 0 × 2⁰ = 0
   
   
   • 1 × 2¹ = 2
   
   
   • 0 × 2² = 0
   
   
   • 1 × 2³ = 8
   
   
   • 0 × 2⁴ = 0
   
   
   • 1 × 2⁵ = 32
   
   
   • Total = 42
   
   
   
   

Alternative Format with Exponents

1. Pick a binary number. Let's use 101. Here is the same method but in a slightly different format. You may find this format easier to understand.
   
   
   
   
   
   
   • 101= (1X2) power of 2 + (0X2) power of 1 + (1X2) power 0
   
   
   • 101= (2X2) + (0X0) + (1)
   
   
   • 101= 4 + 0 + 1
   
   
   • 101= 5
     
     
     
     • The 'zero' is not a number, but its place value must be noted.
     
     
     
     
   
   
   
   

Slot Value

1. Find your number. The example we'll use is 00101010.
   
   
   


2. Read from right to left. With each slot, the values are doubled. The first digit from the right has a value of 1, the second is a 2, then a 4, and so on.
   
   
   


3. Add the values of the ones. The zeros are assigned their correlating number, but those numbers are not added.
   
   
   
   
   
   
   • So, in this example, add 2, 8, and 32. The result is 42.
     
     
     
     • There is a 'no' on 1, a 'yes' on 2, a 'no' on 4, a 'yes' on 8, a 'no' on 16, a 'yes' on 32, a 'no' on 64 and a 'no' on 128. "Yes" means to add, "no" is to skip. You can stop at the last one-digit.
     
     
     
     
   
   
   
   


4. Translate the value into letters or punctuation marks. In addition, you can convert numbers from binary to decimal or convert from decimal to binary.
   
   
   
   
   
   
   • In punctuation marks, the 42 equals an asterisk (*). Click here for a chart.
   
   
   
   

Video

Tips

• Binary counts just like normal numbers. The rightmost digit increments by one until it cannot increase any more (in this case from 0 to 1) and then increments the next digit to the left by one and starts again at zero.


• The numbers we deal with today have a place value. Assuming we are working with whole numbers, the right-most digit is the one's place, the next right-most digit is the ten's place, then hundred's, and so on. The place value for binary numbers go from one's, two's, four's, eight's, and so on.

Related wikiHows

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• How to Find the Greatest Common Divisor of Two Integers


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• How to Estimate the Number of Dots on a Basketball


• How to Convert Within Metric Measurements

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