gf(2) Polynomial long division

c = a/b

a = b01100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 a = 0x65ee6bda0b324559661859ebf3268b49 a = x¹²⁶ + x¹²⁵ + x¹²² + x¹²⁰ + x¹¹⁹ + x¹¹⁸ + x¹¹⁷ + x¹¹⁵ + x¹¹⁴ + x¹¹³ + x¹¹⁰ + x¹⁰⁹ + x¹⁰⁷ + x¹⁰⁵ + x¹⁰⁴ + x¹⁰³ + x¹⁰² + x¹⁰⁰ + x⁹⁹ + x⁹⁷ + x⁹¹ + x⁸⁹ + x⁸⁸ + x⁸⁵ + x⁸⁴ + x⁸¹ + x⁷⁸ + x⁷⁴ + x⁷² + x⁷⁰ + x⁶⁸ + x⁶⁷ + x⁶⁴ + x⁶² + x⁶¹ + x⁵⁸ + x⁵⁷ + x⁵² + x⁵¹ + x⁴⁶ + x⁴⁴ + x⁴³ + x⁴⁰ + x³⁹ + x³⁸ + x³⁷ + x³⁵ + x³³ + x³² + x³¹ + x³⁰ + x²⁹ + x²⁸ + x²⁵ + x²⁴ + x²¹ + x¹⁸ + x¹⁷ + x¹⁵ + x¹¹ + x⁹ + x⁸ + x⁶ + x³ + 1
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
1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1001101010111010011010001110111100001100111101011100001010111111 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 101000101100110101111110101101100011010100100010100100000001101110011000011000010110011110101111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1110000111011100010110010110010011100111010111010100101010010010011000011000010110011110101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 111101101100110001100011000101111101011101010001000100000101101011000011000010110011110101111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11011000111011000001011111110001101101110100100110100101110010111000011000010110011110101111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1000010010101100111111100011110101110111011110001100111011101001000011000010110011110101111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1111000010110100101101101001001111011100011010000110001010110000011000010110011110101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 110101000001110110111100111110011010000100111011010000000001111011000010110011110101111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 10011101010011111010100000101101010110111001110100000101010000111000010110011110101111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 111111101011100000011000010010101110110100011000111111111001000010110011110101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11001000000001001110000101001011110000111101101001111010010111110110011110101111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1010010101111101000100110100100110011110010111110111000111000000110011110101111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11111111000111011110111010011010010010101010101011001101111111110011110101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1100101101001111000011001110101010001100101111100001111010000000011110101111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 101000111110101011001000000010110000000010010111101110000111111011110101111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1110010101000010100000111001000000110001100010011110101100000111110101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 111111111111000111010110111111100111101011111000010100110111000110101111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11001010100101110111110000100010111011000001101100100011100111010101111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1010000001011010001010011001101111000001110111011100001001000100101111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11101011100000010000010111010011001101001010000000000011111011101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1110001001110110110110100111100001110000101010111000001010100011111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 111100011001100101100101001011101111100010111100100000000011100111110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11010110010001100001101110000011111010001001001010000101000011011110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1001100111111000111001101101100111001000110011101000111101100101110011001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1101000010100011100011011011000100001110110100110111011010110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 100101000011001111001010101111000000010001001101011010000001100001001101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11101000100110100010010100110000100010111000101010101010011101001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1110010001000000100110111011111100001110111111101101000110010111101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 111111011111010111100110101000000000010000010110001001100101000101000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11001110100111110001110010011110000100011100011111001001110111001000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1010100001001010111010001110001000111010011001000001011011000111000101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11001011110000100000000000110100110110100100011101010001111000000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1010001011110000110100011011011110101101011001010010011010111110101101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11100001001010101110010101100010100001100100001110010000000001101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1111011100100001000110110001101100010101011011001010010101110011101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 110110110011011011100111111010000011001100110010110011111001100101001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 10000011000110010001111000001110011111111000111000011010010011001001001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11001101000110111011011100001011100110111101111011000111100111001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1010111101000011101111111100100100101110010101100000101001000111001 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11010111111001110101110010011000100010101000111100100011111000001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1001101010111010011010001110111100001100111101011100001010111111 | - 1001101010111010011010001110111100001100111101011100001010111111 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 0 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000001101111001110000111011101111011111000001100011111011011110011011 c_quotient = 0x0000000000000000de70eef7c18fb79b c_quotient = x⁶³ + x⁶² + x⁶⁰ + x⁵⁹ + x⁵⁸ + x⁵⁷ + x⁵⁴ + x⁵³ + x⁵² + x⁴⁷ + x⁴⁶ + x⁴⁵ + x⁴³ + x⁴² + x⁴¹ + x³⁹ + x³⁸ + x³⁷ + x³⁶ + x³⁴ + x³³ + x³² + x³¹ + x³⁰ + x²⁴ + x²³ + x¹⁹ + x¹⁸ + x¹⁷ + x¹⁶ + x¹⁵ + x¹³ + x¹² + x¹⁰ + x⁹ + x⁸ + x⁷ + x⁴ + x³ + x + 1
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 c_remainder = 0x00000000000000000000000000000000 c_remainder = 0