Converting Decimal Numbers to Binary Using Two Methods

Last week, using our knowledge of powers of two, we converted binary numbers using just “1s” and “0s”, into our own decimal base ten numbers. Remember, all data in a computer system consists of binary information. Binary means there are only two possible values: zero and one. Computer software translates between binary information and the information you actually work with on a computer, such as decimal numbers, text, photos, sound and video. Binary information is sometimes also referred to as machine language since it represents the most fundamental level of information stored in a computer system. At a physical level, the zero and ones are stored in the central processing unit of a computer system using transistors. Transistors are microscopic switches that control the flow of electricity. If a current passes through the transistor (the switch is closed), this represents a one. If a current doesn't pass through (the switch is open), this represents a zero.

This week, we focused on the more challenging operation: converting decimal numbers to binary. I taught the children two different methods and they chose to use the one that came easiest to them.

The most popular method is using the descending powers of two with subtraction method. Follow these steps and use the attached pdf to practice converting.

Step 1: Start by making a table of powers of 2 starting with 2^0=1 from right to left.

8,192 4,096 2,048 1,024 512 256 128 64 32 16 8     4      2 1              

Step 2: Look for the greatest power of 2 that is less than your decimal number.

For example, if your decimal number is 41, the largest power of two less than 41 is 32. So 32 gets a “1”

Step 3: Find the difference between your decimal number [41] and the power of two you used in Step 2 [32]. Since the difference between 41 - 32 = 9, we still need on buttons “1s” to make the number 9. 

Step 4: Repeat Steps 2 and 3 until you have all the powers of two that add up to your decimal number. Since we need 9 more, the power of two, 8 gets a “1”; since you have 1 left over, the power of two 1 gets a “1” as well. All of the powers of two in between get a “0”

32 16 8 4 2 1

1 0 1 0 0 1   in base 2 = 41 in decimal base 10

An easier method requires a knowledge of short division which may be too challenging for some children. This is called the Cake Method because it looks like a layered cake as you build each division by two problem. Follow these steps and use the attached pdf to practice up to 8 digit numbers.

Step 1: Choose a decimal number and place it low on the page.

Step 2: Divide that number by 2 using short division. If there is a remainder of 1, place a small 1 in the upper right corner of the next number to be divided. So if you first divide 2 into 5, you get a 2 with a remainder of 1. The one goes on the upper right hand corner of the next number to be divided. If that number is a 2, you are really dividing 2 into 12. 

Step 3: At the end of the division problem, place your remainder to the right of your quotient (the answer to a division problem). 

Step 4: Then divide that quotient by 2 using the same method as Steps 2 and 3 until your quotient is “0” with a remainder of 1.

Step 5: From the top down, your remainders make up your binary number.

Only work with numbers that are comfortable to you and use the attached worksheets to do your work.