Are you trying to convert a set of binary 0s and 1s to a decimal value? There are various simple methods to binary to decimal, but we’ll concentrate on the fastest, least complicated ones! The instructions in this article will show you how to convert a binary to decimal using positional notation, doubling, and a basic Microsoft Excel binary to decimal calculator page.
Continue reading to get a complete guide on how to convert binary to decimal!
How to use Positional Notation
Record the binary number and then list the right-to-left powers of 2
Consider the case when we want to convert the binary value 100110112 to decimal. Make a note of it first. Then, from right to left, list the powers of two. begin at 20 and assign it a value of “1”. For each power, increase the exponent by one. Stop when the number of list elements equals the number of digits in the binary number.
Given that the example number, 10011011, has 8 digits, the list would have the following eight elements: 128, 64, 32, 16, 8, 4, 2, 1
Write the digits of the binary number below their corresponding powers of two
To make each binary digit correspond to its power of 2, simply write 10011011 underneath the numerals 128 (or 128, 64, 32, 16, 8, 4, or 2) and 1 (or 1). The binary number should correspond exactly to the right of the stated powers of two, and so on.
If you’d want, you may also write the binary digits that are higher than the powers of two in that manner. The fact that they match up is crucial.
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Connect the digits in the binary number with their corresponding powers of two
Connect each binary number’s consecutive digits to the power of two that comes after it in the list above by drawing lines, starting from the right. To start, draw a line from the binary number’s initial digit to the list’s first power of two. A line then connects the second binary digit of the number to the second power of the two listed in the list. Connect the next digit to the next power of two, and so on. The relationship between the two sets of statistics will be easier for you to see visually.
Write down the final value of each power of two
Go from one binary digit to the next. The appropriate power of two for the digit, if it is a 1, should be written below the line, underneath the digit. Write a 0 below the line, under the digit, if it is a 0.
It becomes a “1” because “1” is the corresponding number. It becomes a “2” since “2” goes with “1.” “4” becomes “0” since “0” is the inverse of “4”. Because “8” and “16” are correlated with “1,” respectively, they become “8” and “16,” respectively. The numbers “32” and “64” are equivalent to the number “0,” becoming “0,” and “128” is equivalent to the number “1,” becoming “128.”
Add the final values
Add the figures listed below the line now. So what do you do? 128 + 0 + 0 + 16 + 8 + 0 + 2 + 1 = 155. The binary number 10011011 has a decimal equivalent in this.
Write the answer along with its base subscript
Now all you have to do to demonstrate that you are using a decimal answer that must be operating in powers of ten is to write 15510. You’ll find that remembering the powers of two is easier and that you can do the task more rapidly the more you practice converting from binary to decimal.
How to use Doubling
Read further to know more about converting binary to decimal.
Write down the binary number
This approach does not rely on powers. As a result, it is simpler to mentally convert enormous numbers because you just need to keep track of a subtotal. You must first write down the binary number to convert a binary number using the doubling method. Let’s imagine your project’s number is 10110012. Put it on paper.
Starting from the left, double your previous total and add the current digit
Given that you are working with the binary number 10110012, the first digit you see is 1 on the left. You haven’t begun yet. Therefore your prior total is 0. The previous sum, 0, must be multiplied by 2, and the most recent digit, 1, must be added. Your new total is 1 because 0 x 2 Plus 1 equals 1.
Double your current total and add the next leftmost digit
You now have a total of 1, and the new current digit is 0. multiplying by two and adding zero. 1 x 2 + 0 Equals 2. Your new total now is 2.
Repeat the previous step
Next, double your current total by two and add your following digit, 1, to that. 2 x 2 + 1 = 5. Now, you have five total.
Repeat the previous step
Double your current total, 5, then add the following digit, 1, to get 11. 5 x 2 + 1 = 11. Your current tally is 11.
Follow the previous step
2 x 11 + 0 = 22, which is the result of multiplying your current number, 11, by two
Repeat the previous step
Double the amount you have now, 22, and then add the following digit, 0. 22 x 2 + 0 = 44.
Continue doubling your current total and adding the next digit until you’ve run out of digits
You’ve reached your final number and are almost finished! You changed the decimal form of the number 89 from the decimal notation 1001101112. All you need to do is double the 44 you now have by two and then add one for the final digit. 2 x 44 + 1 Equals 89. The task is complete!
Write the answer along with its base subscript
To demonstrate that you’re using a decimal with a base of 10, write your final response as 8910 in your answer.
Use this method to convert from any base to decimal
Given that the number is in base 2, doubling is used. Replace the 2 in the method with the given number’s base if the given number has a different base. As an illustration, you would swap out “x 2” for “x 37” if the given integer was in base 37. Always use decimals when calculating results (base 10).
So, this was a simple guide to help you know how to convert binary to decimal. Consider this post before doing the same!
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