Question

Give an example of a polynomial error, E1(X), that cannot be detected and an example of a polynomial error, E2(X), that can be detected by the CRC generator P(X) = x4 + X2 + 1

Answer 1

Example of polynomial error E1(x) that cannot be detected by the CRC generator P(x) = x4+x2+1.

* Polynomial evrou, £,OW that that cannot be detected CRC egenerator PGK) 204 + x² +1 P(x) = x + x² + 1 => 1.844 +0.X+.+0.x+1.30 by the In linary → 10101 Taking polynomial that is be checked is :- f(x) = x + x² + x + x² + x (11010110) 111 TOTO O O O 1 1 - No need XOR I TOTO (Appended bits bits [ACC]]= 1 4) + 0000 E NO ERROR DETECTED Ex=0 Any 3 bit evror term CE(2) that is an exact multiple of f(x) will not be detected (No errou detection)

Example of polynomial error E2(x) that can be detected by the CRC generator P(x) = x4+x2+1.

* Polynomial error , &₂ (x) that can be detected by the CRC_generator POW) = 24+x² +1 P(x) = x + x² + 1 1.x" to.x3 + 1.x² + o.x't loxo In bils 10101 Taking polynomial that is to be checked is :- M6x) = x + x + x² + x² + 1 Dagc6 + 1.25 +0.22"+1.23 + 1.2? +0.x+1.7° In bits U101101 - Bits to be appender Bits (PCR)-1) =S-1 = (0000) dividend = 110110100009 Divisors 10101

10101 Lolo XOR f TITOLI Il lol ! lololoooo TO101 II 0 1 1 0 ☺100L Olt OHHOO. OHHHO o LO10LV o 10 Ø100 L A @ 10101 XOR o ĐO 0 0 1 1 0 1 Ø 1000 101011 011010 H 10101 lolol OLIO ♡ o lol lo con Tolol Olomo fumor Eremainder detected! Now, this erron will be used was appended bits of MCX). J €2(x) → 10 Потоот 23+x+ T Speriat 1 ENING