Writing a number as a power of 2

Welcome to our YouTube video on writing a number as a power of 2!

In this video, we will be discussing how to write a number as a power of 2. This technique is particularly useful in computer science and engineering, as it can simplify complex mathematical expressions and make them easier to work with.

To begin, let’s review what it means to write a number as a power of 2. In mathematics, a number can be written as a power of another number if it can be expressed in the form a^n, where a is the base and n is the exponent. For example, the number 16 can be written as 2^4, since 2^4 = 16.

So, how do we write a number as a power of 2? The key to this technique is to use the concept of binary numbers. Binary is a number system that uses only two digits, 0 and 1, to represent numbers. In binary, each digit represents a power of 2. The rightmost digit represents 2^0, the next digit represents 2^1, and so on.

To write a number as a power of 2, we can convert the number to binary and use the binary digits to represent the powers of 2. Let’s go through an example to see how it works.

Example 1: Write 48 as a power of 2

To write 48 as a power of 2, we first convert 48 to binary:

48 = 110000 in binary

Next, we use the binary digits to represent the powers of 2. Starting from the rightmost digit, we have:

0 * 2^0 = 0
0 * 2^1 = 0
0 * 2^2 = 0
1 * 2^3 = 8
1 * 2^4 = 16
1 * 2^5 = 32

Adding up these values, we get:

48 = 0 + 0 + 0 + 8 + 16 + 32

So, 48 can be written as:

48 = 2^5 + 2^4 + 2^3

And there we have it – 48 written as a power of 2!

Example 2: Write 120 as a power of 2

To write 120 as a power of 2, we again convert 120 to binary:

120 = 1111000 in binary

Using the binary digits to represent the powers of 2, we have:

0 * 2^0 = 0
0 * 2^1 = 0
0 * 2^2 = 0
1 * 2^3 = 8
1 * 2^4 = 16
1 * 2^5 = 32
1 * 2^6 = 64

Adding up these values, we get:

120 = 0 + 0 + 0 + 8 + 16 + 32 + 64

So, 120 can be written as:

120 = 2^6 + 2^5 + 2^4 + 2^3

And there we have it – 120 written as a power of 2!

You may have noticed that we can also write a number as a sum of powers of 2 that are not necessarily consecutive powers. For example, we could write 48 as 2^5 + 2^2 + 2^1, or as 2^5 + 2^4 + 2^0. The key is to use the binary digits to represent the powers of 2 that add up to the original number.