gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b0000000000000100000000000000000000000000000000000000000000000000 a = 0x0004000000000000 a = x⁵⁰
b = b0000000000000000000000000000000010110000110000010101001011111001 b = 0x00000000b0c152f9 b = x³¹ + x²⁹ + x²⁸ + x²³ + x²² + x¹⁶ + x¹⁴ + x¹² + x⁹ + x⁷ + x⁶ + x⁵ + x⁴ + x³ + 1
100000000000000000000000000000000000000000000000000 | 10110000110000010101001011111001 - 10110000110000010101001011111001 | 1 --------------------------------------------------- | 1100001100000101010010111110010000000000000000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 --------------------------------------------------- | 111001111000100000110010001110100000000000000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------- | 10101110100100101100000110000110000000000000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------- | 11110010100111001001101111111000000000000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 --------------------------------------------------- | 1000010010111011100100100000001000000000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------- | 11010001111010110000001111101100000000000 | - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 --------------------------------------------------- | 1100001001010100101000100010101000000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------- | 111001010010101111100001101001100000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------- | 10101011110101010110011010111110000000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------- | 11011000101000011010001000111000000 | - 00000000000000000000000000000000 | 0 - 00000000000000000000000000000000 | 0 - 10110000110000010101001011111001 | 1 --------------------------------------------------- | 1101000011000001111000011000001000 | - 10110000110000010101001011111001 | 1 --------------------------------------------------- | 110000000000000101100110111101100 | - 10110000110000010101001011111001 | 1 --------------------------------------------------- | 11100001100000000110100000011110 | - 10110000110000010101001011111001 | 1 --------------------------------------------------- | 1010001010000010011101011100111 |
c_quotient = b0000000000000000000000000000000000000000000010111001101111001111 c_quotient = 0x00000000000b9bcf c_quotient = x¹⁹ + x¹⁷ + x¹⁶ + x¹⁵ + x¹² + x¹¹ + x⁹ + x⁸ + x⁷ + x⁶ + x³ + x² + x + 1
c_remainder = b0000000000000000000000000000000001010001010000010011101011100111 c_remainder = 0x0000000051413ae7 c_remainder = x³⁰ + x²⁸ + x²⁴ + x²² + x¹⁶ + x¹³ + x¹² + x¹¹ + x⁹ + x⁷ + x⁶ + x⁵ + x² + x + 1