How to Decode Binary Numbers

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Deciphering a binary sequence of 1s and 0s is a daunting task. However, with a little logic you can decode binary numbers. Humans have adapted to the decimal system (the basic ten number system) simply because we have ten fingers. Computers only have two “fingers” which are 1 and 0 (yes, no or true, false). Therefore, the binary system (the basic two-number system) was born. ^{[1] X Research Source}

Table of Contents

By exponent

Find the binary number you want to convert. We have the following example: 101010 .

Multiply each binary character by 2 exponents ‘x’, where ‘x’ is the row number of the corresponding binary character. ^{[2] X Research Source} Remember: the binary system is analyzed from right to left . ^{[3] X Research Source} 0. From the rightmost row 0. ^{[4] X Research Source}

Add all the results together. Do it 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

Another spelling of the exponent

Choose a binary number. Here we have 101 . This method is similar to the above, only slightly different in writing, even easier to understand.

101= (1X2) to 2 + (0X2) to 1 + (1X2) to 0
101= (2X2) + (0X0) + (1)
101= 4 + 0 + 1
101= 5
- ‘0’ is not a number, it represents a value that needs attention.

Distance value

Find binary numbers. We have for example 00101010 .

Decode from right to left. For each distance, the value will be doubled. The first character from the right has the value 1, the second is 2, the next is 4, and so on. ^{[5] X Research Sources}

Adds all values of 1s. Zeros are also correlated but will not be added.

So, in this example 2 + 8 + 32 = 42.
- After doubling, we get a value of ‘false’ at 1, ‘true’ at 2, ‘false’ at 4, ‘true’ at 8, ‘false’ at 16, ‘true’ at 32, ‘false’ at 64 and ‘false’ at 128. Add the “true” values and ignore the “false” values until the last character.

Decode the value into letters or punctuation. In addition, you can convert numbers from binary to decimal or vice versa.

In punctuation marks, 42 is the asterisk (*). You can see the decoder table here.

Advice

Binary numbers are just like any other regular number. The rightmost numeric character increments by 1 until it can no longer be incremented (in this case from 0 to 1), the next numeric character on the left also increments by 1 and starts over at 0.
The numbers we calculate today all have place symbols. Assuming you’re working with an integer, the rightmost numeric character is the units row, the next numeric character is tens, then hundreds, and so on. The positional notation of the binary number will be calculated from the first, second, third, fourth, five, six, seven, eight, and so on. ^{[6] X Research Source}

Steps

By exponent

Another spelling of the exponent

Distance value

Advice

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