gf(2) mod

c = a % b

Calculate c = a/b, result is c_remainder

gf(2) Polynomial long division

c = a/b

a = b00000000000000000000000000000000010000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a = 0x00000000400000000000000000000000 a = x⁹⁴
b = b00000000000000000000000000000000000000000000000000000000000000001001101010111010011010001110111100001100111101011100001010111111 b = 0x00000000000000009aba68ef0cf5c2bf b = x⁶³ + x⁶⁰ + x⁵⁹ + x⁵⁷ + x⁵⁵ + x⁵³ + x⁵² + x⁵¹ + x⁴⁹ + x⁴⁶ + x⁴⁵ + x⁴³ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³⁴ + x³³ + x³² + x²⁷ + x²⁶ + x²³ + x²² + x²¹ + x²⁰ + x¹⁸ + x¹⁶ + x¹⁵ + x¹⁴ + x⁹ + x⁷ + x⁵ + x⁴ + x³ + x² + x + 1
10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 | 1001101010111010011010001110111100001100111101011100001010111111 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------- | 11010101110100110100011101111000011001111010111000010101111110000000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------- | 1001111011010010010111110010111011010110101101111010111010001110000000000000000000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------- | 10001101000001101111100000111011010010000100110110000110001000000000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------- | 10111101111001001000011010100010001001011100001000100100111110000000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------- | 100111010111101110111001001101001010010011011111100110010001110000000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------- | 1111100000111010001110110111010100000101010010110111010001100000000000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------- | 110001010000000010100111001101000001001101111101011011011011111000000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------- | 10111111011101011001111110110110001111110001000101011110000000100000000000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------- | 100101110011111111011101011001001100111110010010011100101111010000000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------- | 11011000010110110101100010111100001101100111101100000100101100000000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------- | 1000010111000010011000001010011001110101000111011000110000011110000 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------- | 1111101111000000010000100100101111001111010000100111010100001000 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ----------------------------------------------------------------------------------------------- | 110000101111010001010101010010011000011101101111011011110110111 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000010011000010010100001110100011001 c_quotient = 0x000000000000000000000000984a1d19 c_quotient = x³¹ + x²⁸ + x²⁷ + x²² + x¹⁹ + x¹⁷ + x¹² + x¹¹ + x¹⁰ + x⁸ + x⁴ + x³ + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000110000101111010001010101010010011000011101101111011011110110111 c_remainder = 0x0000000000000000617a2aa4c3b7b7b7 c_remainder = x⁶² + x⁶¹ + x⁵⁶ + x⁵⁴ + x⁵³ + x⁵² + x⁵¹ + x⁴⁹ + x⁴⁵ + x⁴³ + x⁴¹ + x³⁹ + x³⁷ + x³⁴ + x³¹ + x³⁰ + x²⁵ + x²⁴ + x²³ + x²¹ + x²⁰ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹³ + x¹² + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁵ + x⁴ + x² + x + 1