ClassX Video Lessons Youtube Channel TutoringHour Converting from Decimal to Binary | Convert Base-10 to Base-2
Welcome to our fun guide on how to convert decimal numbers into binary numbers! We’ll explore two different methods to make this conversion easy and exciting. Let’s dive in by converting the decimal number 25 into binary.
Before we start, let’s list the powers of 2. These will help us break down our decimal number:
Since 32 is greater than 25, we’ll use 24 (16) as our starting point. Subtracting 16 from 25 leaves us with 9. So, 25 can be written as 16 + 9.
Next, let’s break down 9 using powers of 2. We’ll use 23 (8), leaving us with 1 after subtraction. So, 9 is 8 + 1.
Finally, 1 is simply 20.
Now, let’s create a table to help us write the binary number:
Reading from left to right, the binary equivalent of 25 is 11001. This method is called the sum-of-weights method.
Let’s try converting 106 to binary. We’ll list more powers of 2:
We’ll use 26 (64) since it’s less than 106. Subtracting 64 from 106 gives us 42. Next, we’ll use 25 (32) for 42, leaving us with 10. Finally, 10 can be broken down into 23 (8) and 21 (2).
Here’s our table for 106:
The binary equivalent of 106 is 1101010.
Now, let’s learn the double-dabble method, also known as the repeated division method. We’ll convert 115 to binary:
Write the final quotient 1 and the remainders from bottom to top. The binary equivalent of 115 is 1110011.
Now you know two methods to convert decimal numbers to binary! Practice these methods and see which one you like best. Happy converting!
Challenge yourself and your classmates to a race! Convert a list of decimal numbers to binary as quickly as you can using the sum-of-weights method. The first one to finish correctly wins. This will help you practice and speed up your conversion skills.
Use binary numbers to create a piece of art. Assign a binary number to each pixel in a grid, and color the pixels based on whether the binary number is even or odd. This activity will help you visualize binary numbers in a creative way.
Work on a puzzle where you match decimal numbers with their binary equivalents. This will reinforce your understanding of how each decimal number corresponds to a binary number. Try to complete the puzzle without looking at any conversion tables!
Write a short story using binary numbers. Each character or event in your story should be represented by a binary number. Share your story with the class and see if they can decode it. This will help you practice binary conversion in a fun and imaginative way.
Form teams and create secret messages using binary code. Exchange messages with another team and try to decode each other’s messages. This activity will enhance your binary conversion skills and teamwork.
Sure! Here’s a sanitized version of the transcript:
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Hello and welcome to Tutoring Hour! In this video, I’m going to show you two different methods to convert a decimal number into a binary number. Let’s start encoding our first decimal number, 25.
But before we proceed, let’s write down the powers of 2 and look for a power of 2 that is less than or equal to 25.
– 2 to the power of 0 is 1.
– 2 to the power of 1 is 2.
– 2 squared is 4.
– 2 cubed is 8.
– 2 to the fourth is 16.
– 2 to the fifth is 32.
We’ll stop here, as 32 is greater than 25, and go with 2 to the fourth, which is 16. Now, we’ll subtract 16 from 25, which gives us 9. We can decompose 25 as 16 plus 9.
Next, we’ll look for a power of 2 that is less than or equal to 9. We’ll go with 2 cubed, which is 8. Subtracting 8 from 9 leaves us with 1. So, 9 can be written as 8 plus 1.
Now, we’ll look for a power of 2 that is less than or equal to 1. 2 to the power of 0 is 1.
Let’s make a table and write down the place values:
– 2 to the power of 0
– 2 to the power of 1
– 2 squared
– 2 cubed
– 2 to the fourth (the highest power used here)
We’ll write 1 if we’ve used it to decompose our number, and 0 if we haven’t.
– Do we have 2 to the power of 0? Yes, we do. So, we’ll write a 1.
– We don’t have 2 to the first power, so we’ll write 0.
– We don’t have 2 squared, so we’ll write 0 again.
– How about 2 cubed? We do have that, so let’s write 1.
– We also have 2 to the fourth, so we’ll write 1 to represent that.
Let’s compose our string of 0s and 1s. Reading from left to right, we have 11001, the binary equivalent of 25. This method of conversion is known as the sum-of-weights method.
Now, let’s switch to our next number: 106, converting from base-10 to base-2. First, we’ll list out the powers of 2. This will help us while deconstructing the number.
– 2 to the power of 0 is 1.
– 2 to the power of 1 is 2.
– 2 squared is 4.
– 2 cubed is 8.
– 2 to the fourth is 16.
– 2 to the fifth is 32.
We’ll add a few more until we get closer to the number 106, ensuring the number is less than or equal to the given number.
– 2 to the sixth is 64.
– 2 to the seventh is 128 (which exceeds our number).
We’ll go with 2 to the sixth, which is 64. Subtracting 64 from 106 gives us 42. So, 106 can be decomposed as 64 plus 42.
Next, we can break down 42 into powers of 2. We’ll go with 2 to the fifth, which is 32, as it is the nearest. Subtracting 32 from 42 leaves us with 10. So, 42 can now be expressed as 32 plus 10.
Now, we’ll look for a power of 2 that is less than or equal to 10. We have 2 cubed, which is 8. We can redefine 10 as 8 plus 2.
Let’s make our table of place values starting from 2 to the power of 0 to 2 to the sixth.
– Do we have 2 to the power of 0? No, so we write 0.
– We do have 2 to the first, so we’ll write 1 there.
– 2 squared doesn’t appear, so we’ll write 0.
– 2 cubed has been used, so we write 1.
– We don’t have 2 to the fourth, so we write 0.
– 2 to the fifth appears, so we write 1.
– 2 to the sixth also occurs, so we write 0.
Putting our string together from left to right, we have the binary equivalent of 106, which is 1101010.
Now, let me introduce you to the easiest method of converting a decimal number into a binary number, the double-dabble method, or the repeated division method.
Let’s take the number 115 and convert it from base 10 to base 2.
– 115 divided by 2 is 57 (remainder 1).
– Dividing 57 by 2 gives us 28 (remainder 1).
– 28 divided by 2 leaves us with 14 (remainder 0).
– 14 divided by 2 is 7 (remainder 0).
– Dividing 7 by 2 gives us 3 (remainder 1).
– 3 divided by 2 is 1 (remainder 1).
We’ll write the final quotient 1 along with the remainders from the bottom to the top. The encoded binary equivalent of 115 is 1110011.
We’ve covered both methods of converting a decimal number to a binary number. Use the one you are comfortable with and start encoding!
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Thanks for watching Tutoring Hour!
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This version maintains the educational content while ensuring clarity and professionalism.
Decimal – A number system based on ten, using digits from 0 to 9. – Computers often convert decimal numbers into binary to process them.
Binary – A number system that uses only two digits, 0 and 1, to represent data. – The binary code is essential for computers to understand and execute instructions.
Powers – The result of multiplying a number by itself a certain number of times. – In binary, each position represents a power of two.
Convert – To change something into a different form or system. – You can convert a decimal number to binary using a simple algorithm.
Method – A specific procedure or technique used to achieve a result. – The method for sorting data efficiently is crucial in programming.
Number – A mathematical object used to count, measure, and label. – In coding, a number can be stored in different formats like integer or float.
Table – An arrangement of data in rows and columns, often used to organize information. – A truth table helps programmers understand logical operations.
Equivalent – Having the same value, function, or meaning. – The binary number 1010 is equivalent to the decimal number 10.
Remainder – The amount left over after division when one number does not divide the other exactly. – When converting a decimal to binary, the remainder is used to determine the binary digits.
Practice – The repeated exercise of an activity to improve skill. – Regular practice in coding helps students become proficient programmers.
