120 in binary

Guri Bee

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18-10-2024

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120 in Binary: A Step-by-Step Guide

Have you ever wondered how the number 120 is represented in binary, the language computers use? Understanding binary is crucial for anyone interested in programming, computer science, or simply wanting to grasp the fundamentals of how computers work.

This article will break down the process of converting 120 to binary, explaining the underlying principles and offering practical examples.

The Basics of Binary

Binary is a base-2 number system that uses only two digits: 0 and 1. Each position in a binary number represents a power of 2, starting from the rightmost digit (2^0) and increasing by one for each position to the left.

For example, the binary number 1011 translates to:

• 1 x 2^3 (8) + 0 x 2^2 (4) + 1 x 2^1 (2) + 1 x 2^0 (1) = 11 in decimal.

Converting 120 to Binary

To convert 120 to binary, we'll employ the method of repeated division by 2, keeping track of the remainders.

1. Divide 120 by 2: 120 / 2 = 60, remainder 0
2. Divide 60 by 2: 60 / 2 = 30, remainder 0
3. Divide 30 by 2: 30 / 2 = 15, remainder 0
4. Divide 15 by 2: 15 / 2 = 7, remainder 1
5. Divide 7 by 2: 7 / 2 = 3, remainder 1
6. Divide 3 by 2: 3 / 2 = 1, remainder 1
7. Divide 1 by 2: 1 / 2 = 0, remainder 1

Now, read the remainders from bottom to top: 1111000.

Therefore, 120 in binary is 1111000.

Verifying the Result

We can verify this result by converting 1111000 back to decimal:

• 1 x 2^6 (64) + 1 x 2^5 (32) + 1 x 2^4 (16) + 1 x 2^3 (8) + 0 x 2^2 (4) + 0 x 2^1 (2) + 0 x 2^0 (1) = 120.

Real-World Application

This conversion is fundamental in computer science and programming. For instance, when working with digital images, each pixel is represented by a binary value, determining its color. Understanding binary allows us to manipulate these values and process the image accordingly.

Conclusion

Converting 120 to binary might seem complex at first, but following the steps outlined in this article simplifies the process. Mastering binary opens doors to a deeper understanding of computer systems and the logic behind their operations.

Note: This explanation was inspired by and adapted from the following Github resources:

• GitHub Repo: This repository contains a detailed explanation of the binary system and various conversion methods.
• GitHub Issue: This issue discusses the specific conversion of 120 to binary and provides insights from experienced developers.