Read the remainders from bottom-up, this gives the binary equivalent of the given decimal number. Repeat the process until the result is ‘0’. Divide the result with 2 and continue the above process. Write the result below and the remainder on the right-hand side.
To convert a decimal number into binary, divide the number with 2. So, it is important to convert the decimal numbers into binary numbers. But machines like computers and electronic equipment use binary and can only understand the binary data. We use decimal numbers in our day-to-day life calculations and numbering. Digital wireless communication transfers data in the form of binary bits. Digital data is stored in the form of binary bits. In 1937, Shannon published his findings in his thesis, which became the initial point from where the binary system is being used in Digital Logics, Computers, Electric Circuits, etc…Īll modern computers use binary encoding for their instruction set and data storage. Claude Shannon noticed the similarity between the Boolean Algebra and logic of electric circuits. This system was based on binary ON-OFF logic. Is there a "64" written in the equation? Nope! So beneath that arrow, we're going to write a "0.In 1847, George Boole in his paper ‘The Mathematical Analysis of Logic’ described Boolean Algebra. Then, consult the addition problem we wrote down up above, the one that says 128 + 8 + 2 = 138ĭo you see a "128" in that problem? If so, write a "1" underneath the corresponding arrow. Draw a downward-pointing arrow (↓) below each value. And make sure to leave some space between each number.Īs you can see, there are eight individual values listed here. Do this in descending order from left to right. Write out the value of every exponent of 2 beginning with "128" (remember, that's 2 7) and "1" (which equals 2). Our next objective is to add them up.įind a piece of paper if you haven't already done so. This process gave us three important figures: 128, 8 and 2. Like so:Īnd what do you know? The number 2 is equal to 2 1. So at this point, our job is to subtract 8 from 10. The power of 2 which comes the closest to equaling 10 is 2 3, or 8. Next, take that 10 and have a second gander at the exponent list.
Now, we're going to subtract 128 from 138. Find the value that comes the closest to 138 without exceeding it.Ī quick reread tells us 138 sits between 256 (which is 2 8) and 128 (that's 2 7). Have another look at our "powers of 2" list. Here is a handy widget to help you with the conversions. If that doesn't bother you and you'd like to learn more, the Institute of Electrical and Electronics Engineers (IEEE) has published a standardized conversion method.
#BINARY TO DECIMAL CONVERTER FULL#
But full disclosure: It's kind of complicated. There is a technique for converting numbers with a fractional component, like 0.25 and 3.14, into binary.
Congratulations, we've come full circle! Go take a victory lap. All we really have to do is solve this puzzle: We don't need them in an addition problem. What does 0 + 2 + 0 + 8 + 0 + 0 + 0 + 128 equal?īefore we answer that, let's get rid of all those zeroes. Take the results of all those multiplication problems and add them together. Hang on, we're almost at the finish line! If you continue using this pattern, proceeding from the farthermost right to the farthermost left, here's what you'll ascertain: Doing so will give you 0 x 2 2, which equals 0. Let's begin with the 0 on the far right end. Alright, now let's return to the actual conversion.īecause 10001010 contains 8 individual bits, we're going to do 8 separate multiplication problems.
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