170 in binary

Guri Bee

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19-10-2024

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170 in Binary: A Deep Dive

Ever wondered how your computer stores numbers like 170? It's all thanks to the binary system, which uses only two digits: 0 and 1. In this article, we'll break down how to convert 170 into its binary equivalent.

Understanding the Binary System

Binary, or base-2, works differently than our familiar decimal system (base-10). In decimal, each digit's place value is a power of 10 (units, tens, hundreds, etc.). In binary, each digit's place value is a power of 2 (units, twos, fours, eights, etc.).

Example:

The decimal number 1023 can be represented as:

• 1 * 10^3 + 0 * 10^2 + 2 * 10^1 + 3 * 10^0

Similarly, the binary number 1111111111 can be represented as:

• 1 * 2^9 + 1 * 2^8 + 1 * 2^7 + 1 * 2^6 + 1 * 2^5 + 1 * 2^4 + 1 * 2^3 + 1 * 2^2 + 1 * 2^1 + 1 * 2^0

Converting 170 to Binary

There are two main methods for converting decimal numbers to binary:

1. Repeated Division by 2 (The Classic Method)

• Divide 170 by 2: 170 / 2 = 85 (remainder 0)
• Divide 85 by 2: 85 / 2 = 42 (remainder 1)
• Divide 42 by 2: 42 / 2 = 21 (remainder 0)
• Divide 21 by 2: 21 / 2 = 10 (remainder 1)
• Divide 10 by 2: 10 / 2 = 5 (remainder 0)
• Divide 5 by 2: 5 / 2 = 2 (remainder 1)
• Divide 2 by 2: 2 / 2 = 1 (remainder 0)
• Divide 1 by 2: 1 / 2 = 0 (remainder 1)

Now, read the remainders from bottom to top: 10101010. This is the binary representation of 170.

2. Place Value Method

• Find the highest power of 2 less than 170: This is 2^7 (128).
• Subtract 128 from 170: 170 - 128 = 42
• Find the highest power of 2 less than 42: This is 2^5 (32).
• Subtract 32 from 42: 42 - 32 = 10
• Find the highest power of 2 less than 10: This is 2^3 (8).
• Subtract 8 from 10: 10 - 8 = 2
• Find the highest power of 2 less than 2: This is 2^1 (2).
• Subtract 2 from 2: 2 - 2 = 0

Now, look at the powers of 2 you used (2^7, 2^5, 2^3, 2^1) and represent them with 1s in their respective positions. This gives us:

• 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
• 1 0 1 0 1 0 1 0

This again gives us 10101010.

Important Note: Both methods achieve the same result, but the repeated division method might be easier for some people to understand.

Applications of Binary

Understanding binary is crucial for various fields:

• Computer Science: Every computer program is ultimately executed as a series of 0s and 1s.
• Electronics: Digital circuits rely heavily on binary logic to process data.
• Data Compression: Algorithms use binary representations to efficiently store and transmit information.

Final Thoughts

Converting 170 to binary might seem like a simple task, but it serves as a gateway to understanding the foundational concepts of computer science and how computers process information. The binary system, though seemingly abstract, is the core language that powers our digital world.