CRC Calculator
CRC appends the remainder of a modulo-2 division: data 1101011111 with generator 10011 is sent as 11010111110010.
e.g. 10011 or x^4 + x + 1
11010111110010
- CRC (remainder)
- 0010
- Generator bits
- 10011
- CRC length r = degree
- 4
Step-by-step solution
- Append 4 zeros: 11010111110000
- Divide by 10011 using XOR (modulo-2): remainder 0010
- Send data + remainder = 11010111110010
CRC Formula
frame = data · 2ʳ + (data · 2ʳ mod G)
modulo-2 (XOR) division; r = degree of G
Worked Example
Data 1101011111 with generator x⁴ + x + 1 (10011):
- Append 4 zeros: 11010111110000
- Divide by 10011 using XOR (modulo-2): remainder 0010
- Send data + remainder = 11010111110010
Generator bits: 10011 · CRC length r = degree: 4
GATE tip
Append r zeros before dividing, where r is the generator’s degree (one less than its number of bits). Forgetting this is the most common mistake.
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Frequently asked questions
Which errors does a CRC detect?
All single-bit errors, all double-bit errors for a suitable generator, any odd number of errors if x + 1 divides G, and all burst errors up to r bits long.
How do I convert a generator polynomial to bits?
Write a 1 for each power present: x⁴ + x + 1 → 10011 (powers 4, 1, 0).
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). CRC Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/crc-calculator/
IEEE
Scientific Converters, "CRC Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/crc-calculator/