How to Convert Decimals to Binary Numbers Using Excel

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To undertake this activity there is an expectation that students have an understanding of binary numbers and how to count in binary. Refer to the introduction to binary lesson. Use the following table with headings to show the progression of the binary numeral system much like 1s, 10,for decimal system. Binary is a doubling pattern of 1, 2, 4, 8, 16 etc. Use the table to ensure all students can count in binary and represent decimal numbers in binary.

Note remember to start from the left when using the table to make a decimal number. For example to make the number 31 do I need a 16, YES. Do I need and 8, NO. Do I need a 4, YES. Do I need a 2, NO. Do I need a 1, YES. So the binary number is From binary to decimal excel this process for other numbers. Try making numbers Ask from binary to decimal excel the largest number than can be made in this table. How can we make from binary to decimal excel number ? Discuss the pattern of doubling to get 64 and and add these two new columns.

Scaffold the learning by providing a spread sheeting file which has the set up partly completed. The files provided are MS Excel. Some students who are well skilled in using a spreadsheet can design their own converter and may not need a file to scaffold their learning.

Provide this file for students that have a basic understanding of how to use a spreadsheet. As a starting point ask students to test the sheet to see how it from binary to decimal excel. Ask students if they can make their converter work up to the decimal number of For students who want to add a conditional if statement to automatically represent o or 1 as on or off, use this file.

A completed version might look similar to this, see the file here. For students that are interested in creating an interface refer to this example. Refer to this version of the completed spreadsheet with tips that explain how the sheet is set up. This version includes binary cards with dots, which can be used as a further challenge. Computers today use the binary system to represent information.

It is called binary because only two different digits are used. It is also known as base two normally we use base Each zero or one is called a bit binary digit. A group of eight bits is called a byte. Suggested steps Prior knowledge To undertake this activity there is an expectation that students have an understanding of binary numbers and how to count in binary.

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In the text proper, we saw how to convert the decimal number While this worked for this particular example, we'll need a more systematic approach for less obvious cases. In fact, there is a simple, step-by-step method for computing the binary expansion on the right-hand side of the point.

We will illustrate the method by converting the decimal value. Begin with the decimal fraction and multiply by 2. The whole number part of the result is the first binary digit to the right of the point. So far, we have. Next we disregard the whole number part of the previous result the 1 in this case and multiply by 2 once again. The whole number part of this new result is the second binary digit to the right of the point. We will continue this process until we get a zero as our decimal part or until we recognize an infinite repeating pattern.

Disregarding the whole number part of the previous result this result was. The whole number part of the result is now the next binary digit to the right of the point.

So now we have. In fact, we do not need a Step 4. We are finished in Step 3, because we had 0 as the fractional part of our result there. You should double-check our result by expanding the binary representation. The method we just explored can be used to demonstrate how some decimal fractions will produce infinite binary fraction expansions.

Next we disregard the whole number part of the previous result 0 in this case and multiply by 2 once again. Disregarding the whole number part of the previous result again a 0 , we multiply by 2 once again. We multiply by 2 once again, disregarding the whole number part of the previous result again a 0 in this case. We multiply by 2 once again, disregarding the whole number part of the previous result a 1 in this case. We multiply by 2 once again, disregarding the whole number part of the previous result.

Let's make an important observation here. Notice that this next step to be performed multiply 2. We are then bound to repeat steps , then return to Step 2 again indefinitely. In other words, we will never get a 0 as the decimal fraction part of our result. Instead we will just cycle through steps forever.

This means we will obtain the sequence of digits generated in steps , namely , over and over. Hence, the final binary representation will be. The repeating pattern is more obvious if we highlight it in color as below: