gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000000000000000001001011111101011011111101011100110001 a = 0x00000012fd6fd731 a = x³⁶ + x³³ + x³¹ + x³⁰ + x²⁹ + x²⁸ + x²⁷ + x²⁶ + x²⁴ + x²² + x²¹ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹⁴ + x¹² + x¹⁰ + x⁹ + x⁸ + x⁵ + x⁴ + 1
b = b0000000000000000000000000000000111010111111001010000011000111110 b = 0x00000001d7e5063e b = x³² + x³¹ + x³⁰ + x²⁸ + x²⁶ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x¹⁸ + x¹⁶ + x¹⁰ + x⁹ + x⁵ + x⁴ + x³ + x² + x
1001011111101011011111101011100110001 | 111010111111001010000011000111110 - 111010111111001010000011000111110 | 1 ------------------------------------- | 111110000011001111111011010011010001 | - 111010111111001010000011000111110 | 1 ------------------------------------- | 100111100000101111000010100100001 | - 000000000000000000000000000000000 | 0 - 000000000000000000000000000000000 | 0 - 111010111111001010000011000111110 | 1 ------------------------------------- | 11101011111100101000001100011111 |
c_quotient = b0000000000000000000000000000000000000000000000000000000000011001 c_quotient = 0x0000000000000019 c_quotient = x⁴ + x³ + 1
c_remainder = b0000000000000000000000000000000011101011111100101000001100011111 c_remainder = 0x00000000ebf2831f c_remainder = x³¹ + x³⁰ + x²⁹ + x²⁷ + x²⁵ + x²⁴ + x²³ + x²² + x²¹ + x²⁰ + x¹⁷ + x¹⁵ + x⁹ + x⁸ + x⁴ + x³ + x² + x + 1