# How to Read Binary

Three Methods:With ExponentsAlternative Format with ExponentsSlot Value

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

### Method 1 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 × 2
^{0}= 0 - 1 × 2
^{1}= 2 - 0 × 2
^{2}= 0 - 1 × 2
^{3}= 8 - 0 × 2
^{4}= 0 __1 × 2__^{5}= 32- Total = 42

- 0 × 2

### Method 2 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.

### Method 3 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.

- So, in this example, add 2, 8, and 32. The result is 42.
- 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.

## 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.

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