How to convert binary to decimal
In computer science and digital circuit design, binary and decimal are the two most commonly used representations of numbers. Binary is composed of 0 and 1 and is the basic language of computers; while decimal is the counting method commonly used in our daily lives. This article will introduce in detail how to convert binary numbers to decimal numbers, and provide structured data and examples to help understanding.
1. Basic concepts of binary and decimal systems
Binary is a counting system based on 2, and each bit can only be 0 or 1. For example, the binary number 1010 represents 10 in decimal. Decimal is a counting system based on 10, and each digit can be a number between 0 and 9.
2. Method of converting binary to decimal
Convert a binary number to a decimal number by following these steps:
1. Number each bit of the binary system from right to left, starting from 0.
2. Multiply the value of each bit (0 or 1) by 2 raised to the power of the bit number.
3. Add all results to get the final decimal number.
The following is an example table of binary to decimal conversion:
| Binary bit | Bit number (n) | Calculated as (value × 2ⁿ) | result |
|---|---|---|---|
| 1 | 3 | 1 × 2³ | 8 |
| 0 | 2 | 0 × 2² | 0 |
| 1 | 1 | 1 × 2¹ | 2 |
| 0 | 0 | 0 × 2⁰ | 0 |
| sum | 10 |
As can be seen from the above table, the result of converting the binary number 1010 to decimal is 10.
3. More examples
For further understanding, here are more binary to decimal examples:
| binary number | Conversion steps | decimal result |
|---|---|---|
| 1101 | 1×2³ + 1×2² + 0×2¹ + 1×2⁰ | 13 |
| 10000 | 1×2⁴ + 0×2³ + 0×2² + 0×2¹ + 0×2⁰ | 16 |
| 1111 | 1×2³ + 1×2² + 1×2¹ + 1×2⁰ | 15 |
4. Frequently Asked Questions
Q1: Why are binary numbers numbered from right to left?
A1: Because the lowest bit of binary (the rightmost bit) represents 2⁰, followed by 2¹, 2², etc. to the left, this is consistent with the weight of decimal digits.
Q2: Can binary numbers represent negative numbers?
A2: Yes, binary can represent negative numbers through complement, but this article only discusses the conversion of unsigned binary.
Q3: How to quickly verify the conversion results?
A3: You can use a calculator or a programming language (such as Pythonint('1010', 2)) for quick verification.
5. Summary
Converting binary to decimal is a basic skill in computer science. Mastering this method helps to understand the underlying working principle of the computer. Through the steps and examples in this article, I believe readers will be able to complete this conversion skillfully. If you want to learn more, you can try converting decimal to binary, or explore conversion methods for other bases (such as hexadecimal).
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