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사용자:up_down(비교)

r138 vs r139
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1111000 1111000 1111000 101000 110010 101001 1100011001000000 100000 1010110000011001 1100011101000000 100000 1101011000010101 1101000011011100 1011100001011100 100000 1101010001011100 1010111000110000 1101010101011100 1011001011100100 101110 100000 1100011000001000 1011100101111100 100000 1011010011100100 1100010110110100 100000 110010 1011001010010100 100000 1101010101011100 100000 1100011110010000 1011100110101100 100000 1100011000101100 1011100000100100 1100000100011100 100000 110001 110000 101000 110010 101001 101100 100000 110110 1100011101000000 100000 110001 110001 110000 101000 110010 101001 1100011101110100 100000 1011010000011100 1011001011100100 101110 100000 1010110111111000 100000 1100011001111000 1100010111010000 100000 1100001000101011 1100011110010000 100000 1011000001011101 1100010111010000 100000 1100010101000100 1011011110011000 1100110010101000 1100011110010000 1011100001011100 100000 110010 1011100101111100 100000 1100011110010001 1100000100110001 1101010101011000 1100010111101100 100000 110001 110001 110000 110000 101100 101100 110010 101100 101100 1100110010011000 1011011111111100 100000 110010 1100100111000100 1100001000011000 1100011110000100 1100011101000100 100000 1011000010011000 1101000011000000 1011000010110100 1011001010010100 100000 1011110000101001 1100001011011101 1011001111000100 100000 1100011110001000 1011001011100100 101110 100000 1100111011110100 1101010011101000 1101000100110000 100000 1010110011110101 1101010101011001 1100011101000100 100000 1100100000000100 1010110011110101 1101010101011000 1011001010010100 100000 1100000010101100 1011011110001100 1011010011100100 100000 1100100100010001 1100010111010000 1011001010010100 100000 1100011101110100 1100100111000100 1100001000011000 1011100101111100 100000 1100010011110000 1010110011100000 100000 1011010010100100 1100010111010000 100000 1000010 1011100101111100 100000 1011110110011001 1100011101110100 1011001010010100 100000 1010110010111101 1100011010110000 1011001111000100 100000 1100011110001000 1011001010010100 1011001101110000 101100 100000 1100011101110100 1011001010010100 100000 1100010110110100 1100000101001000 1011111000010100 1011100110101100 1100010110110100 1100010111010000 1100000100011100 100000 110010 1100100111000100 1100001000011000 1011100101111100 100000 1011000010011000 1101000011000000 1011000010111100 100000 1011010101001100 100000 110001 110001 110000 110000 1000010 100000 1101011000010101 1100001011011101 1100011100111100 1011100001011100 100000 1100011110010001 1100000100110001 1101010101011000 1010111000110000 100000 1011010101001100 1011101100111000 1100011101110100 1011001011100100 101110 100000 1011111001000100 1100001010110111 1101010101011000 1010110010001100 100000 1101010100000100 1011100001011100 1010110111111000 1011011110011000 1011101000111000 1100011101011000 100000 1010110010111101 1100011010110000 100000 1011101010000111 1011101010000111 100000 1101010100000100 1011100001011100 1010110111111000 1011011110011000 1011110000001101 100000 1100010110111000 1100010110110100[* 1010110111111000 [[C(프로그래밍 언어)| 1000011 1100010110111000 1100010110110100]] 1010110000000000 100000 1011110000010100 1100011101110100 1011000100001000 1011100110101100 100000 1011100110101100 1101000100110000 1011011111110100 1100011101000100 100000 1100100111000000 1100011011010000 1101010101011000 1100100111000000 100000 1100010101001010 1010111000110000 100000 1011010101001100 1011101100111000 1100010111010000 100000 1100000010101100 1100001011100100 100000 1011001100000000 1100100100010001 1100100000000001 1100011101111000 100000 1101010001011100 1101011000000100 1100011101110100 1011011101111100 1010110011100000 100000 1101010101011000 1010111000110100 100000 1101011110011000 1011010011100100 1011001011100100 101110 100000 1100100110001001 100000 1100011101110100 100000 1011110000101001 1100001011011101 1100011101000100 100000 1100010011110000 1100100111000000 100000 1100010101001010 1011001010010100 100000 1101010100000100 1011100001011100 1010110111111000 1011011110011000 1011101000111000 1011001111000100 100000 1011100111001110 1011001011100100 1011001010010100 100000 1011100111010000 101110 100000 1101010100000100 1011100001011100 1010110111111000 1011011110011000 1011101000111000 1011010011100100 1100011101000000 100000 1011010100010100 1011110010000100 1010111001000101 101100 100000 1011100110101100 1011110010000100 1100001011110001 101100 100000 1011001101100100 1101010101010001 100000 1011010011110001 100000 1100011000101000 1010110000010110 100000 1100011101111100 1100010111010000 1011001010010100 100000 1100100011111100 1011100001011100 100000[[16진법|110001 110110 1100100111000100 1011110010010101]] 1100011101000100 100000 1100000010101100 1100011010101001 1101010101011000 1010111000110000 1011001111000100 100000 1101010101011000 1010110011100000 101110 101110 101110 101110 1011101 1100010111010000 1100000100011100 100000 1100010011110000 1011001010010100 100000 1011110000101001 1100001011011101 1011001100000000 1011100001011100 100000 110000 1100010 110001 110001 110000 110000 1100110010011000 1011011111111100 100000 1100010101011110 1100010111010000 100000 110000 1100010 1011100101111100 100000 1011110110011001 1101011110001000 1010111000110000 1011001111000100 100000 1101010101011100 1011001011100100 101110 100000 1101001010111001 1101011110001000 1011000010011000 100000 110100 1100011110010000 1011100110101100 1100010100101001 100000 1011011101000100 1100011011001100 1100000100011100 100000 1100011101111101 1011001010010100 1011001011100100 1011101001110100 100000 110001 110000 110000 100101 100000 1100111011110100 1010110011110101 1010110011111100 101110
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전자 기기에서 음수는 첫 자리(가장 높은 자리)의 수가 1인 것으로 나타낸다. 즉 첫 번째 숫자가 0이면 양수이고, 1이면 음수이다. 이건 그냥 컴퓨터의 정수 표기법에 대한 약속이고 진법 자체와는 관련이 없다. 1의 보수(1's complement, 1'C)[* 補數, complement], 2의 보수(2's complement, 2'C) 등의 방식이 있으며, 컴퓨터에서 가장 널리 사용하는 것은 2의 보수이다. 1의 보수는 양수에서 모든 비트를 반전시켜서 표현하는 것이고, 여기에 1을 더한 것이 2의 보수이다. 예를 들어보면 다음과 같다.
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* {{{0000 0101}}} = 숫자 5
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* {{{1111 1010}}} = 비트 반전 (1의 보수에서의 -5)
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* {{{1111 1011}}} = 비트 반전에 1을 더함 (2의 보수에서의 -5)
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1의 보수에서는 0000 0000과 1111 1111이 모두 0이 되므로 0이 두 가지로 표현되는 문제가 생긴다. 2의 보수 표기는 10진수와 상호 변환하기 가장 어려운 표기법이긴 하나[* 그래봤자 별거 없다. 비트 반전시키고 1 더하면 끝이다.], 연산에서 양수와 음수를 똑같이 취급할 수 있다는 엄청난 이점이 있다.
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1100100000000100 1100011110010000 100000 1010111000110000 1010111000110000 1100010111010000 1100000100011100 100000 1100011101001100 1100001000011000 1011001010010100 100000 1100110010101011 100000 1100011110010000 1011100110101100 101000 1010110000000000 1100011110100101 100000 1011000110010010 1100011101000000 100000 1100011110010000 1011100110101100 101001 1100011101011000 100000 1100001000011000 1010110000000000 100000 110001 1100011101111000 100000 1010110010000011 1100011100111100 1011100001011100 100000 1011000010011000 1101000011000000 1011000010111000 1011001011100100 101110 100000 1100100110001001 100000 1100110010101011 100000 1011110010001000 1100100111111000 100000 1100001000101011 1100011110010000 1010110000000000 100000 110000 1100011101110100 1011101001110100 100000 1100010110010001 1100001000011000 1100011101110100 1010110011100000 101100 100000 110001 1100011101110100 1011101001110100 100000 1100011101001100 1100001000011000 1100011101110100 1011001011100100 101110 100000 1100011101110100 1010110001110100 100000 1010110111111000 1011000011100101 100000 1100111011110100 1101010011101000 1101000100110000 1100011101011000 100000 1100100000010101 1100001000011000 100000 1101010001011100 1010111000110000 1011110010010101 1100010111010000 100000 1011001100000000 1101010101011100 100000 1100010101111101 1100000110001101 1100011101110100 1010110011100000 100000 1100100111000100 1011110010010101 100000 1100011110010000 1100110010110100 1100011001000000 1011001010010100 100000 1010110100000000 1011100000101000 1100011101110100 100000 1100010111000110 1011001011100100 101110 100000 110001 1100011101011000 100000 1011110011110100 1100001000011000 101000 110001 100111 1110011 100000 1100011 1101111 1101101 1110000 1101100 1100101 1101101 1100101 1101110 1110100 101100 100000 110001 100111 1000011 101001[* 1000100011011100 110010101111000 101100 100000 1100011 1101111 1101101 1110000 1101100 1100101 1101101 1100101 1101110 1110100 1011101 101100 100000 110010 1100011101011000 100000 1011110011110100 1100001000011000 101000 110010 100111 1110011 100000 1100011 1101111 1101101 1110000 1101100 1100101 1101101 1100101 1101110 1110100 101100 100000 110010 100111 1000011 101001 100000 1011010011110001 1100011101011000 100000 1011110000101001 1100001011011101 1100011101110100 100000 1100011110001000 1100011100111100 1011101001110000 101100 100000 1100111011110100 1101010011101000 1101000100110000 1100010111010000 1100000100011100 100000 1010110000000000 1100011110100101 100000 1011000100010000 1011100110101100 100000 1100000010101100 1100011010101001 1101010101011000 1011001010010100 100000 1010110010000011 1100011101000000 100000 110010 1100011101011000 100000 1011110011110100 1100001000011000 1100011101110100 1011001011100100 101110 100000 110001 1100011101011000 100000 1011110011110100 1100001000011000 1011001010010100 100000 1100010110010001 1100001000011000 1100010111010000 1100000100011100 100000 1011101010101000 1011010011100000 100000 1011111001000100 1101001010111000 1011100101111100 100000 1011110000011000 1100100000000100 1100001011011100 1100111100011100 1100000100011100 100000 1101010001011100 1101011000000100 1101010101011000 1011001010010100 100000 1010110010000011 1100011101110100 1010110011100000 101100 100000 1100010111101100 1010111000110000 1100010111010000 100000 110001 1100011101000100 100000 1011001101010100 1101010101011100 100000 1010110010000011 1100011101110100 100000 110010 1100011101011000 100000 1011110011110100 1100001000011000 1100011101110100 1011001011100100 101110 100000 1100011000001000 1011100101111100 100000 1011010011100100 1100010110110100 1011110011110100 1011101001110100 100000 1011001011100100 1100011101001100 1010110011111100 100000 1010110000011001 1011001011100100 101110
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* {{{110000 110000 110000 110000 100000 110000 110001 110000 110001}}} 100000 111101 100000 1100001000101011 1100011110010000 100000 110101
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* {{{110001 110001 110001 110001 100000 110001 110000 110001 110000}}} 100000 111101 100000 1011111001000100 1101001010111000 100000 1011110000011000 1100100000000100 100000 101000 110001 1100011101011000 100000 1011110011110100 1100001000011000 1100010111010000 1100000100011100 1100011101011000 100000 101101 110101 101001
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* {{{110001 110001 110001 110001 100000 110001 110000 110001 110001}}} 100000 111101 100000 1011111001000100 1101001010111000 100000 1011110000011000 1100100000000100 1100010111010000 100000 110001 1100011101000100 100000 1011001101010100 1101010101101000 100000 101000 110010 1100011101011000 100000 1011110011110100 1100001000011000 1100010111010000 1100000100011100 1100011101011000 100000 101101 110101 101001
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예를 들어 3 + (-5)를 한다고 하자. 2의 보수 표기법에서는 0000 0011 + 1111 1011이 되고 계산해 보면 1111 1110 = -2가 된다. 마치 둘 다 양수인 양 더했더니 올바른 값이 나와버렸다. 이는 음수+음수도 마찬가지다. -5 + (-7) = 1111 1011 + 1111 1001 = 1 1111 0100 = 1111 0100 = -12이다. 다른 어떤 음수 표기법도 부호 확인 없이 때려 넣으면 저렇게 정답이 나오지 않는다. 이렇게 연산 과정에서 부호를 고려할 필요가 없다는 점은 속도에 약간의 이익을 주는데, 덧셈과 뺄셈이라는 연산은 CPU 내에서 10진수로 출력하기 따위와는 비교가 불가능할 정도로 많이 하는 연산이므로 컴퓨터는 내부적으로 2의 보수 표기법을 쓴다. 다만 이 방식은 그 대가로 치명적인 오류를 안고 있어서 미리 방지하는 것이 필수이다.
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110001 1100011101011000 100000 1011110011110100 1100001000011000 1100010111010000 1100000100011100 1011001010010100 100000 110000 110000 110000 110000 100000 110000 110000 110000 110000 1010110011111100 100000 110001 110001 110001 110001 100000 110001 110001 110001 110001 1100011101110100 100000 1011101010101000 1011010001010000 100000 110000 1100011101110100 100000 1011010000011000 1011101111000000 1011100001011100 100000 110000 1100011101110100 100000 1011010001010000 100000 1010110000000000 1100100111000000 1011100001011100 100000 1101010001011100 1101011000000100 1011010000011000 1011001010010100 100000 1011101100111000 1100100000011100 1010110000000000 100000 1100000011011101 1010111000110100 1011001011100100 101110 100000 110010 1100011101011000 100000 1011110011110100 1100001000011000 100000 1101010001011100 1010111000110000 1011001010010100 100000 110001 110000 1100100111000100 1100001000011000 1100011001000000 100000 1100000011000001 1101011000111000 100000 1011110011000000 1101011001011000 1101010101011000 1010111000110000 100000 1010110000000000 1100011110100101 100000 1100010110110100 1011100000100100 1100011010110100 100000 1101010001011100 1010111000110000 1011110010010101 1100011101110100 1010111000110100 100000 1101010101011000 1011000010011000[* 1010110111111000 1011011110011000 1011110100100100 1100011110010000 100000 1011110011000100 1010110001110000 100000 1100010111000110 1011001011100100 101110 100000 1011111001000100 1101001010111000 100000 1011110000011000 1100100000000100 1100001011011100 1101000010100100 1010110011100000 100000 110001 100000 1011001101010100 1101010101011000 1011101001110100 100000 1011000001011101 1100011101110100 1011001011100100 101110] 101100 100000 1100010111110000 1100000010110000 1100010111010000 1100000100011100 100000 1100010110010001 1100001000011000 1100011001000000 100000 1100011101001100 1100001000011000 1011100101111100 100000 1011011000010001 1010110000011001 1100011101110100 100000 1100110111101000 1010111000001001 1101010101100000 100000 1100001000011000 100000 1100011110001000 1011001011100100 1011001010010100 100000 1100010111000100 1100110010101101 1011000010011100 100000 1100011101110100 1100100000010000 1100011101110100 100000 1100011110001000 1011001011100100 101110
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일단 전기 신호가 들어온다, 안 들어온다라는 식으로 쉽게 구현할 수 있어서 전자 기기, 특히 컴퓨터에서 사용한다. 그리고 고등학교 수학 과정의 지수/로그 파트에 출현해 수험생을 괴롭힌다. 물론 쫄지 말고 10진법처럼 계산하면 생각보다는 쉽게 풀리긴 한다.
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1100011000001000 1011100101111100 100000 1011010011100100 1100010110110100 100000 110011 100000 101011 100000 101000 101101 110101 101001 1011100101111100 100000 1101010101011100 1011001011100100 1010110011100000 100000 1101010101011000 1100011110010000 101110 100000 110010 1100011101011000 100000 1011110011110100 1100001000011000 100000 1101010001011100 1010111000110000 1011110010010101 1100010111010000 1100000100011100 1011001010010100 100000 110000 110000 110000 110000 100000 110000 110000 110001 110001 100000 101011 100000 110001 110001 110001 110001 100000 110001 110000 110001 110001 1100011101110100 100000 1011010000011000 1010110011100000 100000 1010110011000100 1100000010110000 1101010101110100 100000 1011110011110100 1011101001110100 100000 110001 110001 110001 110001 100000 110001 110001 110001 110000 100000 111101 100000 101101 110010 1010110000000000 100000 1011010000011100 1011001011100100 101110 100000 1011100111001000 1100111001011000 100000 1011010001011000 100000 1011001011100100 100000 1100010110010001 1100001000011000 1100011101111000 100000 1100010110010001 100000 1011001101010100 1101010110001000 1011001101010100 1011001011001000 100000 1100011000101100 1011110000010100 1011100101111000 100000 1010110000010010 1100011101110100 100000 1011000010011000 1100011001000000 1011110010000100 1011100000111000 1011001011100100 101110 100000 1100011101110100 1011001010010100 100000 1100011101001100 1100001000011000 101011 1100011101001100 1100001000011000 1011001111000100 100000 1011100111001000 1100110000101100 1010110000000000 1100100111000000 1011001011100100 101110 100000 101101 110101 100000 101011 100000 101000 101101 110111 101001 100000 111101 100000 110001 110001 110001 110001 100000 110001 110000 110001 110001 100000 101011 100000 110001 110001 110001 110001 100000 110001 110000 110000 110001 100000 111101 100000 110001 100000 110001 110001 110001 110001 100000 110000 110001 110000 110000 100000 111101 100000 110001 110001 110001 110001 100000 110000 110001 110000 110000 100000 111101 100000 101101 110001 110010 1100011101110100 1011001011100100 101110 100000 1011001011100100 1011100101111000 100000 1100010110110100 1011010110100100 100000 1100011101001100 1100001000011000 100000 1101010001011100 1010111000110000 1011110010010101 1011001111000100 100000 1011110110000000 1101011000111000 100000 1101011001010101 1100011101111000 100000 1100010111000110 1100011101110100 100000 1011010101001100 1011100000100100 100000 1011000100100011 1100011100111100 1011101001110100 100000 1100100000000000 1011100000000111 1010110010001100 100000 1100100000010101 1011001011110101 1100011101110100 100000 1011000010011000 1100011000100100 1100100111000000 100000 1100010101001010 1011001010010100 1011001011100100 101110 100000 1100011101110100 1011100000000111 1010110010001100 100000 1100010111110000 1100000010110000 100000 1010110011111100 1100100000010101 1100010111010000 1100000100011100 100000 1011110110000000 1101011000111000 1011100101111100 100000 1010110011100000 1011100000100100 1101010101100000 100000 1101010101000100 1100011010010100 1010110000000000 100000 1100010111000110 1011001011100100 1011001010010100 100000 1100100000010000 1100011101000000 100000 1100000110001101 1011001111000100 1100010111010000 100000 1100010101111101 1010110000000100 1100011101011000 100000 1100011101110100 1100011101110101 1100011101000100 100000 1100100011111100 1011001010010100 1011001101110000 101100 100000 1011001101100111 1100000101001000 1010110011111100 100000 1011111010000100 1100000101001000 1100011101110100 1011011101111100 1011001010010100 100000 1100010111110000 1100000010110000 1100011101000000 100000 1000011 1010000 1010101 100000 1011000010110100 1100010111010000 1100000100011100 100000 110001 110000 1100100111000100 1100001000011000 1011100001011100 100000 1100110110011100 1011100000100101 1101010101011000 1010111000110000 100000 1011010100110000 1100011100000100 1100011001000000 1011001010010100 100000 1011111001000100 1010110101010000 1010110000000000 100000 1011110110001000 1010110000000000 1011001010100101 1101010101100000 100000 1100100000010101 1011001111000100 1011100001011100 100000 1011100111001110 1100011101110100 100000 1101010101011000 1011001010010100 100000 1100010111110000 1100000010110000 1100011101110100 1011101111000000 1011100001011100 100000 1100111011110100 1101010011101000 1101000100110000 1011001010010100 100000 1011000010110100 1011110110000000 1100100000000001 1100011100111100 1011100001011100 100000 110010 1100011101011000 100000 1011110011110100 1100001000011000 100000 1101010001011100 1010111000110000 1011110010010101 1100011101000100 100000 1100010011110100 1011001011100100 101110 100000 1011001011100100 1011100111001100 100000 1100011101110100 100000 1011110000101001 1100001011011101 1100011101000000 100000 1010110111111000 100000 1011001100000000 1010110000000000 1011100001011100 100000 1100111001011000 1011101010000101 1100100000000001 1100011101111000 100000 1100011000100100 1011100101011000 1011100101111100 100000 1100010101001000 1010110011100000 100000 1100011110001000 1100010110110100 1100000100011100 100000 1011101111111000 1011100110101100 100000 1011110000101001 1100100111000000 1101010101011000 1011001010010100 100000 1010110010000011 1100011101110100 100000 1101010101000100 1100001000011000 1100011101110100 1011001011100100 101110
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1100011101111100 1011001011101000 100000 1100100000000100 1010111000110000 100000 1100001011100000 1101011000111000 1010110000000000 100000 1011010011100100 1100010110110100 1100011000101000 1011001011100100 101100 100000 1100010101001000 100000 1011010011100100 1100010110110100 1100011000101000 1011001011100100 1011011101111100 1011001010010100 100000 1100001011011101 1100011100111100 1011100001011100 100000 1100001001111101 1010110010001100 100000 1010110101101100 1101011000000100 1101010101100000 100000 1100001000011000 100000 1100011110001000 1100010110110100 1100000100011100 100000 1100100000000100 1100011110010000 100000 1010111000110000 1010111000110000 101100 100000 1101001010111001 1101011110001000 100000 1100111011110100 1101010011101000 1101000100110000 1100010111010000 1100000100011100 100000 1100000010101100 1100011010101001 1101010101011100 1011001011100100 101110 100000 1010110111111000 1011100110101100 1010110011100000 100000 1010110011100000 1011010011110001 1101010101011001 1010110101010000 100000 1100001000011000 1101010101011001 100000 1010110011111100 1100100000010101 1100011101011000 100000 1100100111000000 1100001000011000 101111 1011100001011100 1010110111111000 100000 1101001100001100 1101001010111000 1100010111010000 100000 1100110110011100 1101011000000100 1101010101110100 100000 1100001000011000 1101010111011000 1100000011011101 1100011101000100 100000 1010110100110100 1011100001101101 1101011110001100 1011001011100100 101110 100000 1011101100111100 1011100001100000 100000 1100101011000100 1100100111000000 100000 1011100111010000 1010110011100000 100000 110001 110000 1100100111000100 1011110010010101 1100110010011000 1011011111111100 100000 1010110011000100 1100000010110000 1101010101011000 1011101001110100 100000 1100000011011101 1010110000000001 1011110011110100 1011001011100100 1011001010010100 100000 1100001001111101 1010110010001100 100000 1101010010000000 1011100110101100 1010111000110100 100000 1101010101011100 1011001011100100 101110
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한편, 위에서 볼 수 있듯이 2진법은 0과 1만으로 숫자를 표기하다보니 숫자가 조금만 커져도 엄청난 수의 0과 1이 반복되는 아찔함을 선사한다. 그만큼 사람이 보기 빡세지는데, 요 가독성을 좀 높여보고자 [[16진법]]으로 바꿔서 표현하기도 한다.
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변환하는 방법을 설명하자면, 10001011111011001010110101001100110101001011010110101101011001,,2,, 라는 숫자가 있다고 하자. 이를 뒤에서(일의 자리부터) 4자리씩 끊어서 (00)10 0010 1111 1011 0010 1011 0101 0011 0011 0101 0010 1101 0110 1011 0101 1001로 만든 뒤 4자리씩 16진법으로 변환해서 적으면 된다. 변환 결과는 22FB2B53352D6B59,,16,,. 이것도 여전히 길어 보이지만 이렇게 바꾸면 길이가 4분의 1로 줄어들고 읽기도 그나마 편해진다.
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