CRC Binary Division Calculator

Introduction

CRC (Cyclic Redundancy Check) is an error-detecting code that is used to detect errors during data transmission. The CRC is calculated by dividing the data by a fixed divisor polynomial. The remainder of this division is then appended to the original data and transmitted. At the receiver side, the data is divided by the same divisor polynomial. If the remainder of the division is zero, then the data is error-free.

Calculation of CRC using Binary Division

There are different ways to calculate the CRC, and one of them is using binary division. In binary division, we divide binary numbers using the same process that we use for decimal numbers. However, the main difference is that we only have two digits, 0 and 1, instead of ten digits. To calculate the CRC using binary division, we follow the following steps: 1. Append zeroes to the data to make its length equal to the length of the divisor polynomial minus one. 2. Divide the data by the divisor polynomial using binary division. 3. The remainder of the division is the CRC.

Example of CRC Calculation using Binary Division

Let's take an example to understand the CRC calculation using binary division. Suppose we have the data 11010010 and the divisor polynomial 1001. Step 1: Append zeroes to the data to make its length equal to the length of the divisor polynomial minus one. 11010010000 Step 2: Divide the data by the divisor polynomial using binary division. 1 0 0 1 | 1 1 0 1 0 0 1 0 0 0 1 0 0 1 -------------- 1 1 0 1 0 0 1 ------ 1 1 1 0 0 1 ------ 1 1 1 1 0 0 1 ------ 1 1 1 0 1 0 0 1 ------ 1 1 0 1 Step 3: The remainder of the division is the CRC. CRC = 1101 Therefore, the CRC for the data 11010010 using the divisor polynomial 1001 is 1101.

Conclusion

In conclusion, CRC is an error-detecting code that is widely used in data transmission. The CRC is calculated by dividing the data by a fixed divisor polynomial using binary division. The remainder of this division is then appended to the original data and transmitted. At the receiver side, the data is divided by the same divisor polynomial. If the remainder of the division is zero, then the data is error-free.