How to calculate hexadecimal
In computer science and digital electronics, hexadecimal is a commonly used number system. It uses 16 symbols to represent numerical values, namely 0-9 and A-F (representing 10-15). Hexadecimal is widely used in programming, memory address representation, and color coding. This article will introduce the hexadecimal calculation method in detail and provide structured data to help understanding.
1. Basic knowledge of hexadecimal system
Hexadecimal is a base 16 number system, and the weight of each digit is a power of 16. The following is a comparison table between hexadecimal, decimal and binary:
| hexadecimal | decimal | binary |
|---|---|---|
| 0 | 0 | 0000 |
| 1 | 1 | 0001 |
| 2 | 2 | 0010 |
| 3 | 3 | 0011 |
| 4 | 4 | 0100 |
| 5 | 5 | 0101 |
| 6 | 6 | 0110 |
| 7 | 7 | 0111 |
| 8 | 8 | 1000 |
| 9 | 9 | 1001 |
| A | 10 | 1010 |
| B | 11 | 1011 |
| C | 12 | 1100 |
| D | 13 | 1101 |
| E | 14 | 1110 |
| F | 15 | 1111 |
2. Convert hexadecimal to decimal
Converting a hexadecimal number to decimal is to multiply the value of each bit by the corresponding power of 16 from right to left and then sum. For example:
| hexadecimal number | Calculation process | decimal result |
|---|---|---|
| 1A3 | 1×16² + A×16¹ + 3×16⁰ = 256 + 160 + 3 | 419 |
| FF | F×16¹ + F×16⁰ = 240 + 15 | 255 |
3. Convert decimal to hexadecimal
The way to convert a decimal number to hexadecimal is to keep dividing by 16 and record the remainder until the quotient is 0, and finally arrange the remainder in reverse order. For example:
| decimal number | Calculation process | hexadecimal result |
|---|---|---|
| 500 | 500÷16=31 more than 4; 31÷16=1 more than 15 (F); 1÷16=0 more than 1 | 1F4 |
| 128 | 128÷16=8 more than 0; 8÷16=0 more than 8 | 80 |
4. Hexadecimal operations
The addition, subtraction, multiplication and division operations of hexadecimal numbers are similar to those of decimal, but it should be noted that the rules for carry and borrow are based on 16. Here is an example of addition:
| Addition example | Calculation process | result |
|---|---|---|
| 2A+3B | A+B=15 (F in hexadecimal, carry 1); 2+3+1=6 | 65 |
| FF+1 | F+1=16 (hexadecimal is 0, carry 1); F+1=16 (0, carry 1) | 100 |
5. Application scenarios of hexadecimal system
1.Programming and memory addresses: Computer memory addresses are usually expressed in hexadecimal, such as 0x7FFF.
2.Color coding: Web page colors use hexadecimal RGB values, such as #FFFFFF representing white.
3.data representation: Binary data is often displayed in hexadecimal form for easy reading and debugging.
6. Frequently Asked Questions
Q: Why is hexadecimal commonly used in computer science?
A: Hexadecimal can express binary data concisely (every 4 binary digits corresponds to 1 hexadecimal digit), and is easier to read than binary.
Q: How to quickly convert hexadecimal to binary?
A: You can refer to the comparison table in the first part of this article, or remember that each hexadecimal digit corresponds to 4 binary digits.
Through the above content, I believe you have mastered the basic calculation methods of hexadecimal. In practical applications, proficient use of hexadecimal will greatly improve work efficiency!
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