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 = b00000000000000000000000000000000000000000000000000000000000000001101111001110000111011101111011111000001100011111011011110011011 b = 0x0000000000000000de70eef7c18fb79b b = 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
1100101111011100110101111011010000010110011001001000101010110010110011000011000010110011110101111110011001001101000101101001001 | 1101111001110000111011101111011111000001100011111011011110011011 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1010110101100001110010100001111010111111010110011110100101001110011000011000010110011110101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 111001100010001001001001110100101111110110101100101111011010101011000011000010110011110101111110011001001101000101101001001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1110000101001010100111001001010011110000100011000010100011000111000011000010110011110101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11111100111010011100100110001100110001000000111001111101011100000011000010110011110101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 100010100110010010011101111011000001011000000111001010111010110011000010110011110101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 10101000001010001110011000110111101011110001000100111000011011111000010110011110101111110011001001101000101101001001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1110110010110000000100011000000011011101001111010001111111101001000010110011110101111110011001001101000101101001001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11001011000000111111110111011100011100101100101010100001110010000010110011110101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 10101011100110001001100101011101100110100010100010110010100110010110011110101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1110101111010000111011110101010010110111010011100000101000000100110011110101111110011001001101000101101001001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11010110100000000000011010001101110110110000011011110110011111110011110101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1000111100001110100001111010000110101000100101000001111001000011110101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 101000101111110011010010101011001101001000110111010100111011000110101111110011001001101000101101001001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11111001000110000111100010110110001001110111000111001000010101010101111110011001001101000101101001001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 100111011010001001011001000001111001101111111001111111110011100101111110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 10000111101001010110111111100000101101001110110010010001010001001111110011001001101000101101001001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1011001110101011000000100010111011101010110001100100110110111111111110011001001101000101101001001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 110110111011011111011001101100100101011010010011111101000100100111110011001001101000101101001001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1011100011100110111010001011001011100011100010000111101001011110011001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 110011010010110000001100100010100100010000001111100110111000101011001001101000101101001001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 100110101110011100010011111011000010110000000001011000001000111001001101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 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0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 10000111000101011011101001011101100010111011010100111000110110101000101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1011001011001010101010010101010010010100011101010001111010000011000101101001001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 110110010111010010001111010001101010101111110101010100100011000000101101001001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1110000010001100001101100010110101001111010111001011010101100101101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 11111011111100110110001101101010001110110100110000001011111110101001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 100101100000111000110110011101111110101100001110111100011000011001001 | - 0000000000000000000000000000000000000000000000000000000000000000 | 0 - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 10010000111111011011000100000000010101010000001010001100001110101001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1001110100011010101111111110111100101001000110100111011101000011001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 100001101101010010100010001100011101000100101011100000011011000001 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 10110001010010001001100110001100001000010100100001101100010101101 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 1101111001110000111011101111011111000001100011111011011110011011 | - 1101111001110000111011101111011111000001100011111011011110011011 | 1 ------------------------------------------------------------------------------------------------------------------------------- | 0 |
c_quotient = b00000000000000000000000000000000000000000000000000000000000000001001101010111010011010001110111100001100111101011100001010111111 c_quotient = 0x00000000000000009aba68ef0cf5c2bf c_quotient = 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
c_remainder = b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 c_remainder = 0x00000000000000000000000000000000 c_remainder = 0