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더 보기

사용자:up_down(비교)

r145 vs r146
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4545
|| '''10진수 표기''' || 1024 || 512 || 256 || 128 || 64 || 32 || 16 || 8 || 4 || 2 || 1 ||
4646
||<bgcolor=#765432> '''2진수 표기''' || 10000000000 || 1000000000 || 100000000 || 10000000 || 1000000 || 100000 || 10000 || 1000 || 100 || 10 || 1 ||
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== BCD 코드 ==
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binary-coded decimal(이진화 십진법)의 약어이며, 10진수의 각 자리수를 모두 분리해서 각각 2진수 형태로 표현한 것이다.
48
== 1000010 1000011 1000100 100000 1100111101010100 1011010011011100 ==
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10진수의 한 숫자를 표현하기 위해서 BCD로 총 4자리의 2진수가 된다. 즉 10진수의 모든 숫자를 각각 0000{0,,10,,} ~ 1001{9,,10,,}로 옮길 수 있으며, 이때 나머지 1010 ~ 1111는 사용하지 않는다.
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1100010 1101001 1101110 1100001 1110010 1111001 101101 1100011 1101111 1100100 1100101 1100100 100000 1100100 1100101 1100011 1101001 1101101 1100001 1101100 101000 1100011101110100 1100100111000100 1101011001010100 100000 1100001011101101 1100100111000100 1011110010010101 101001 1100011101011000 100000 1100010101111101 1100010110110100 1100011101110100 1011101001110000 101100 100000 110001 110000 1100100111000100 1100001000011000 1100011101011000 100000 1010110000000001 100000 1100011110010000 1011100110101100 1100001000011000 1011100101111100 100000 1011101010101000 1011010001010000 100000 1011110110000100 1011100110101100 1101010101110100 1100000100011100 100000 1010110000000001 1010110000000001 100000 110010 1100100111000100 1100001000011000 100000 1101011000010101 1101000011011100 1011100001011100 100000 1101010001011100 1101011000000100 1101010101011100 100000 1010110010000011 1100011101110100 1011001011100100 101110
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표기 방식은 각 자릿수마다 해당하는 4자리 2진수로 변환하면 된다.
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ex) 365,,10,, ==> 0011^^(1)^^ 0110^^(2)^^ 0101^^(3)^^,,BCD,,
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(1) = 100의 자리 / (2) = 10의 자리 / (3) = 1의 자리
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110001 110000 1100100111000100 1100001000011000 1100011101011000 100000 1101010101011100 100000 1100001000101011 1100011110010000 1011100101111100 100000 1101010001011100 1101011000000100 1101010101011000 1010111000110000 100000 1100011100000100 1101010101110100 1100000100011100 100000 1000010 1000011 1000100 1011100001011100 100000 1100110100011101 100000 110100 1100011110010000 1011100110101100 1100011101011000 100000 110010 1100100111000100 1100001000011000 1010110000000000 100000 1011010000011100 1011001011100100 101110 100000 1100100110001001 100000 110001 110000 1100100111000100 1100001000011000 1100011101011000 100000 1011101010101000 1011010011100000 100000 1100001000101011 1100011110010000 1011100101111100 100000 1010110000000001 1010110000000001 100000 110000 110000 110000 110000 1111011 110000 101100 101100 110001 110000 101100 101100 1111101 100000 1111110 100000 110001 110000 110000 110001 1111011 111001 101100 101100 110001 110000 101100 101100 1111101 1011100001011100 100000 1100011000101110 1010111000111000 100000 1100001000011000 100000 1100011110001000 1100011100111100 1011101001110000 101100 100000 1100011101110100 1011010101001100 100000 1011000010011000 1011101000111000 1100100111000000 100000 110001 110000 110001 110000 100000 1111110 100000 110001 110001 110001 110001 1011001010010100 100000 1100000010101100 1100011010101001 1101010101011000 1100100111000000 100000 1100010101001010 1011001010010100 1011001011100100 101110
5653
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이렇게 되면 덧셈이 중요해지는데, 그냥 2진수 덧셈이랑 같은 방식으로 하는데, 만약 특정 자릿수가 9를 초과하면 0110,,BCD,, = 6,,10,,을 더해주면 된다.[* 이는 위에 언급되었던 사용하지 않는 표현 1010,,BCD,, ~ 1111,,BCD,,을 건너뛰기 위함.]
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ex) 56 + 48 = 0101 0110,,BCD,, + 0100 1000,,BCD,,
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= 1001 1110,,BCD,, + 0000 0110,,BCD,,
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= 1010 0100,,BCD,, = 104,,10,,
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1101010001011100 1010111000110000 100000 1011110000101001 1100001011011101 1100011101000000 100000 1010110000000001 100000 1100011110010000 1011100110111111 1100001000011000 1011100111001000 1011001011100100 100000 1101010101110100 1011001011111001 1101010101011000 1011001010010100 100000 110100 1100011110010000 1011100110101100 100000 110010 1100100111000100 1100001000011000 1011100001011100 100000 1011110011000000 1101011001011000 1101010101011000 1011101001110100 100000 1011010000011100 1011001011100100 101110 1010 1100101 1111000 101001 100000 110011 110110 110101 101100 101100 110001 110000 101100 101100 100000 111101 111101 111110 100000 110000 110000 110001 110001 1011110 1011110 101000 110001 101001 1011110 1011110 100000 100000 110000 110001 110001 110000 1011110 1011110 101000 110010 101001 1011110 1011110 100000 100000 110000 110001 110000 110001 1011110 1011110 101000 110011 101001 1011110 1011110 101100 101100 1000010 1000011 1000100 101100 101100 1010 101000 110001 101001 100000 111101 100000 110001 110000 110000 1100011101011000 100000 1100011110010000 1011100110101100 100000 101111 100000 101000 110010 101001 100000 111101 100000 110001 110000 1100011101011000 100000 1100011110010000 1011100110101100 100000 101111 100000 101000 110011 101001 100000 111101 100000 110001 1100011101011000 100000 1100011110010000 1011100110101100
6155
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초기 공학용 계산기 등에서 사용되었다. 얼핏 보기에는 비효율적일 수도 있지만 정밀한 소수를 다뤄야 할 때에는 2진수와 10진수를 변환하면서 손실이 발생하는 것이 불가피하기 때문에 BCD를 사용하는 경우도 있다. 이걸 제대로 처리하지 못해서 발생한 문제가 2010년 문제이다.
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1100011101110100 1011100000000111 1010110010001100 100000 1011010000011000 1011101001110100 100000 1011001101100111 1100000101001000 1100011101110100 100000 1100100100010001 1100011010010100 1101010101110100 1100100111000000 1011001010010100 1011001101110000 101100 100000 1010110111111000 1011000011100101 100000 110010 1100100111000100 1100001000011000 100000 1011001101100111 1100000101001000 1100011101110100 1011011110010001 100000 1010110000011001 1100011101000000 100000 1011110000101001 1100001011011101 1100011100111100 1011100001011100 100000 1101010101011000 1011001010010100 1011001101110000 101100 100000 1011100111001100 1100010101111101 100000 1101001010111001 1100100000010101 100000 1100011110010000 1011100110111111 1100001000011000 1010110000000000 100000 111001 1011100101111100 100000 1100110100001000 1010110011111100 1101010101011000 1011101001110100 100000 110000 110001 110001 110000 101100 101100 1000010 1000011 1000100 101100 101100 100000 111101 100000 110110 101100 101100 110001 110000 101100 101100 1100011101000100 100000 1011001101010100 1101010101110100 1100100011111100 1011101001110100 100000 1011010000011100 1011001011100100 101110[* 1100011101110100 1011001010010100 100000 1100011100000100 1100010111010000 100000 1100010110111000 1010111000001001 1011010000011000 1100010111001000 1011001101011000 100000 1100000010101100 1100011010101001 1101010101011000 1100100111000000 100000 1100010101001010 1011001010010100 100000 1101010001011100 1101011000000100 100000 110001 110000 110001 110000 101100 101100 1000010 1000011 1000100 101100 101100 100000 1111110 100000 110001 110001 110001 110001 101100 101100 1000010 1000011 1000100 101100 101100 1100011101000100 100000 1010110001110100 1011000100001000 1011011011110000 1010111000110000 100000 1100011100000100 1101010101101000 101110]
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이 코드를 확장한 IBM에서 만든 EBCDIC 코드도 존재하며 256가지의 문자를 표현할 수 있다.
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1100101 1111000 101001 100000 110101 110110 100000 101011 100000 110100 111000 100000 111101 100000 110000 110001 110000 110001 100000 100000 110000 110001 110001 110000 101100 101100 1000010 1000011 1000100 101100 101100 100000 101011 100000 110000 110001 110000 110000 100000 100000 110001 110000 110000 110000 101100 101100 1000010 1000011 1000100 101100 101100 1010 111101 100000 110001 110000 110000 110001 100000 100000 110001 110001 110001 110000 101100 101100 1000010 1000011 1000100 101100 101100 100000 101011 100000 110000 110000 110000 110000 100000 100000 110000 110001 110001 110000 101100 101100 1000010 1000011 1000100 101100 101100 1010 111101 100000 110001 110000 110001 110000 100000 100000 110000 110001 110000 110000 101100 101100 1000010 1000011 1000100 101100 101100 100000 111101 100000 110001 110000 110100 101100 101100 110001 110000 101100 101100
6559
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1100110100001000 1010111000110000 100000 1010110011110101 1101010101011001 1100011010101001 100000 1010110011000100 1100000010110000 1010111000110000 100000 1011010011110001 1100010111010000 1100000100011100 100000 1100000010101100 1100011010101001 1011010000011000 1100010111001000 1011001011100100 101110 100000 1100010110111100 1101010101001111 100000 1011110011110100 1010111000110000 1100010111010000 1011001010010100 100000 1011111001000100 1101011010101000 1100011100101000 1100100000000001 1100011101111100 100000 1100001000011000 1011001111000100 100000 1100011110001000 1100100111000000 1011100111001100 100000 1100100000010101 1011110000000000 1101010101011100 100000 1100000110001100 1100001000011000 1011100101111100 100000 1011001011100100 1011100100000100 1100010101111100 100000 1101010101100000 100000 1011010101001100 1100010111010000 1011001010010100 100000 110010 1100100111000100 1100001000011000 1100011001000000 100000 110001 110000 1100100111000100 1100001000011000 1011100101111100 100000 1011110011000000 1101011001011000 1101010101011000 1011101001110100 1100000100011100 100000 1100000110010000 1100001011100100 1100011101110100 100000 1011110000011100 1100000011011101 1101010101011000 1011001010010100 100000 1010110010000011 1100011101110100 100000 1011110110001000 1010110000000000 1101010100111100 1101010101011000 1010111000110000 100000 1011010101001100 1011101100111000 1100010111010000 100000 1000010 1000011 1000100 1011100101111100 100000 1100000010101100 1100011010101001 1101010101011000 1011001010010100 100000 1010110010111101 1100011010110000 1011001111000100 100000 1100011110001000 1011001011100100 101110 100000 1100011101110100 1010110001111000 100000 1100100000011100 1011001100000000 1011100001011100 100000 1100110010011000 1011100110101100 1101010101011000 1100100111000000 100000 1011101010111011 1101010101110100 1100000100011100 100000 1011110000011100 1100000011011101 1101010101011100 100000 1011101100111000 1100100000011100 1010110000000000 100000 110010 110000 110001 110000 1011000101000100 100000 1011101100111000 1100100000011100 1100011101110100 1011001011100100 101110
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1100011101110100 100000 1100111101010100 1011010011011100 1011100101111100 100000 1101011001010101 1100011110100101 1101010101011100 100000 1001001 1000010 1001101 1100010111010000 1100000100011100 100000 1011100111001100 1011010011100000 100000 1000101 1000010 1000011 1000100 1001001 1000011 100000 1100111101010100 1011010011011100 1011001111000100 100000 1100100001110100 1100011110101100 1101010101011000 1011101001110000 100000 110010 110101 110110 1010110000000000 1100100111000000 1100011101011000 100000 1011101100111000 1100011110010000 1011100101111100 100000 1101010001011100 1101011000000100 1101010101100000 100000 1100001000011000 100000 1100011110001000 1011001011100100 101110
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== 기타 ==
6765
>'''세상엔 10종류의 사람이 있다. 이진법을 이해하는 사람과 그러지 못하는 사람--, 그리고 이게 설마 삼진법이라고 생각하지 못한 사람--.'''
6866
> (There are 10 types of people in the world; those that understand BINARY, and those who don't--, and those who didn't expect this number to be TERNARY--.)
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