1.1 µðÁöÅаú ¾Æ³¯·Î±×: ±âº» °³³ä
¾Æ³¯·Î±×
: ¿¬¼ÓÀûÀÎ °ª
µðÁöÅÐ
: ÀÌ»êÀûÀÎ °ª
[ ¾Æ³¯·Î±×¹æ¼Û °ú µðÁöÅ»¹æ¼ÛÀÇ Àü°è°µµ Ư¼º ºñ±³]
[¾Æ³¯·Î±× Àü¾Ð°è ¿Í µðÁöÅ» Àü¾Ð°èÀÇ ºñ±³]
1.2 µðÁöÅÐ ½Ã½ºÅÛÀÇ ¿ª»ç
¢º1640³â´ë Pascal ±â°èÀûÀÎ µ¡¼À±â¸¦ ¼³°è
¢º1670³â´ë Gottfried °ö¼À°ú ³ª´°¼ÀÀ» ÇÏ´Â ±â°è¸¦ °³¹ß
¢º1800³â´ë Babbage ÄÄÇ»ÅÍÀÇ È¿½Ã·Î ¾Ë·ÁÁ® ÀÖ´Â ÀÚµ¿ °è»ê±â°è °í¾È
¢º1800³â´ë Boole ÇöÀç ºÎ¿ï ´ë¼öÇÐÀ̶ó ºÎ¸£´Â Ư¼öÇÑ ´ë¼öÇÐ È®¸³
¢º1940³â´ë Áø°ø°ü ½Ã´ë
¢º1950~60³â´ë Æ®·£Áö½ºÅÍ ½Ã´ë
¢º1960³â´ë Áß¹Ý ÁýÀûȸ·Î °³¹ß
¢º1970³â´ë Intel
ÃÖÃÊÀÇ ¸¶ÀÌÅ©·Î ÇÁ·Î¼¼¼ °³¹ß
1.3 µðÁöÅÐ ½Ã½ºÅÛÀÇ °³¿ä
¡Ü µðÁöÅÐ ¼³°è => °èÃþÀû ±¸Á¶
ºÎÇ°(C,
L, TR) => ±âÃÊȸ·Î(GATE) => SSI(0~9) => MSI(10~99) => LSI(1000~)....
ȸ·Î ¼³°èÀÚ ³í¸®¼³°èÀÚ
½Ã½ºÅÛ ¼³°èÀÚ
1.4 ¼ö ü°è
1.4.1 10Áø¼ö(decimal number) : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ÀÇ 10°¡Áö ¼ýÀÚµéÀÇ Á¶ÇÕ
(7 x 10ÀÇ 2½Â) + (8 x 10ÀÇ 1½Â) + (9 x 10ÀÇ 0½Â) = 78910
(7 x 100) + (8 x 10) + (9 x 1) = 78910
1.4.2 2Áø¼ö(binary number) : 0, 1ÀÇ 2°¡Áö ¼ýÀÚÀÇ Á¶ÇÕ
- 110012 ÀÇ 10Áø¼ö Ç¥Çö
(1 x 2ÀÇ 4½Â) + (1 x 2ÀÇ 3½Â) + (0 x 2ÀÇ 2½Â) + (0 x 2ÀÇ 1½Â) + (1 x 2ÀÇ 0½Â)
16 + 8 + 0 + 0 + 1 = 2510
1.4.3 8Áø¼ö(octal number) : 0, 1, 2, 3, 4, 5, 6, 7 ÀÇ 8°¡Áö ¼ýÀÚµéÀÇ Á¶ÇÕ
- 1238 ÀÇ 10Áø¼ö Ç¥Çö
(1 x 8ÀÇ 2½Â) + (2 x 8ÀÇ 1½Â) + (3 x 8ÀÇ 0½Â)
64 +
16 +
3 = 8310
1.4.4 16Áø¼ö(hexadecimal number) :
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F ÀÇ 16°¡Áö ¼ýÀÚµéÀÇ Á¶ÇÕ
- AF1216 ÀÇ 10Áø¼ö Ç¥Çö
(A x 16ÀÇ 3½Â) + (F x 16ÀÇ 2½Â) + (1 x 16ÀÇ 1½Â) + (2 x 16ÀÇ 0½Â)
10 x 4096 + 16 x 256 + 1 x 16 + 2 x 1
40960 + 4096 + 16 + 2 = 4507416
[¿¹Á¦ 1.1] 10011.1012´Â ÇϳªÀÇ 2Áø¼ö¸¦ Ç¥ÇöÇÑ´Ù. ÀÌ ¼öÀÇ 10Áø¼ö °ªÀ» ±¸Ç϶ó.
[¿¹Á¦ 1.2] 234.568 ´Â ÇϳªÀÇ 8Áø¼ö¸¦ ³ªÅ¸³½´Ù. À̼öÀÇ 10Áø¼ö °ªÀ» ±¸Ç϶ó.
[¿¹Á¦ 1.3] ABC.12316 ´Â ÇϳªÀÇ 16Áø¼ö¸¦ ³ªÅ¸³½´Ù. À̼öÀÇ 10Áø¼ö °ªÀ» ±¸Ç϶ó.
1.4.5 Áø¼ö r ¿¡¼ÀÇ °è»ê
ÀÓÀÇÀÇ
Áø¼ö r·Î Ç¥ÇöµÈ ¼öÀÇ ¹®ÀÚ¼¼Æ®´Â r°³°¡ Á¸ÀçÇÑ´Ù.
2Áø¼ö ¿¹¿¡¼ 10Áø¼ö 0¿¡¼ 3±îÁö ¼¿ °æ¿ì, À̸¦ 2Áø¼ö·Î ¾²¸é 00, 01, 10,
11ÀÌ µÈ´Ù.
2Áø¼öÀÇ ÇÑÀÚ¸®¸¦ ºñÆ®(bit : binary digitÀÇ ÁÙÀÎ ¸»)¶ó°í ÇÑ´Ù.
Áï
ºñÆ®¶õ
2Áø¼ö 10¿¡¼ 1°ú 0 °¢°¢À» ÀǹÌÇÑ´Ù.
Áø¼ö | ¹®ÀÚ¼¼Æ®
--------------------------------------------------
2 | 0, 1
--------------------------------------------------
3 | 0, 1, 2
--------------------------------------------------
4 | 0, 1, 2, 3
--------------------------------------------------
:
--------------------------------------------------
8 | 0, 1, 2, 3, 4, 5, 6,
7
--------------------------------------------------
:
--------------------------------------------------
10 | 0, 1, 2, 3, 4, 5, 6, 7,
8, 9
--------------------------------------------------
:
--------------------------------------------------
16 | 0, 1, 2, 3, 4, 5, 6, 7,
8, 9, A, B, C, D, E, F
--------------------------------------------------
[¿¹Á¦ 1.4] 4Áø¼ö¿¡¼ 0ºÎÅÍ 910±îÁö ¼ö¸¦ ¼¼¾î¶ó.
[¿¹Á¦ 1.5] 8Áø¼ö¿¡¼ 0ºÎÅÍ 2010±îÁö ¼ö¸¦ ¼¼¾î¶ó.
[¿¹Á¦ 1.6] 16Áø¼ö¿¡¼ 0ºÎÅÍ 2010±îÁö ¼ö¸¦ ¼¼¾î¶ó.
1.5 Áø¼ö º¯È¯
Á¤º¸¸¦ ó¸®ÇÏ´Â °úÁ¤¿¡¼´Â Áø¼öÀÇ º¯È¯ÀÌ ÇÊ¿äÇϸç
µðÁöÅРó¸®/¿¬»ê(2Áø¼ö) <=> »ç¶÷ÀÇ ±â´É(10Áø¼ö)
2Áø¼ö
: µðÁöÅаü·ÃÀÇ ´ëºÎºÐ¿¡ »ç¿ë
8Áø¼ö, 16Áø¼ö : 2Áø¼ö¸¦ »ç¶÷ÀÌ ÀÌÇØÇϱ⠽±µµ·Ï ª°Ô º¯È¯
--------------------------------------------------
10Áø¼ö | 2Áø¼ö
| 8Áø¼ö |
16Áø¼ö
--------------------------------------------------
0
0000
00
0
--------------------------------------------------
1
0001
01
1
--------------------------------------------------
2
0010
02
2
--------------------------------------------------
3
0011
03
3
--------------------------------------------------
4
0100
04
4
--------------------------------------------------
5
0101
05
5
--------------------------------------------------
6
0110
06
6
--------------------------------------------------
7
0111
07
7
--------------------------------------------------
8
1000
10
8
--------------------------------------------------
9
1001
11
9
--------------------------------------------------
10
1010
12
A
--------------------------------------------------
11
1011
13
B
--------------------------------------------------
12
1100
14
C
--------------------------------------------------
13
1101
15
D
--------------------------------------------------
14
1110
16
E
--------------------------------------------------
15
1111
17
F
--------------------------------------------------
[ 10Áø¼ö, 2Áø¼ö, 8Áø¼ö, 16Áø¼öÀÇ µî°¡ Ç¥Çö]
1.5.1 2Áø¼öÀÇ 16Áø¼ö·ÎÀÇ º¯È¯
2Áø¼ö ÇüÅ·ΠǥÇöµÈ °¢ ºñÆ®¸¦ ¼Ò¼ýÁ¡À» ±âÁØÀ¸·Î ÁÂ, ¿ìÃøÀ¸·Î 4ÀÚ¸®¾¿ ²÷¾î
»ó±â 10Áø¼ö, 2Áø¼ö, 8Áø¼ö, 16Áø¼öÀÇ µî°¡ Ç¥Çö TableÀ» ÀÌ¿ë, °¢ °ªÀ» ±¸ÇÏ¸é µÈ´Ù.
[¿¹Á¦ 1.7] 2Áø¼ö 101111011111.011110002 ¸¦ 16Áø¼ö·Î º¯È¯Ç϶ó.
[¿¹Á¦ 1.8] 2Áø¼ö 1111100001111110.100110112 ¸¦ 16Áø¼ö·Î º¯È¯Ç϶ó.
1.5.2 16Áø¼ö¿Í 8Áø¼öÀÇ 2Áø¼ö·ÎÀÇ º¯È¯
16Áø¼öÀÇ ÇÑÀÚ¸®´Â 2Áø¼öÀÇ 4ÀÚ¸®¿¡ ÇØ´çÇÑ´Ù.
»ó±â 10Áø¼ö, 2Áø¼ö, 8Áø¼ö, 16Áø¼öÀÇ µî°¡ Ç¥Çö TableÀ» ÀÌ¿ë, °¢ °ªÀ» ±¸ÇÏ¸é µÈ´Ù.
8Áø¼öÀÇ °æ¿ì¿¡´Â 8Áø¼öÀÇ °¢ ÇÑÀÚ¸®¼ö°¡ 2Áø¼öÀÇ 3ÀÚ¸®¿¡ ÇØ´çÇÔÀ¸·Î
»ó±â 10Áø¼ö, 2Áø¼ö, 8Áø¼ö, 16Áø¼öÀÇ µî°¡ Ç¥Çö TableÀ» ÀÌ¿ë, °¢ °ªÀ» ±¸ÇÏ¸é µÈ´Ù.
[¿¹Á¦ 1.9] 16Áø¼ö A12B.E616À» 2Áø¼ö·Î º¯È¯Ç϶ó.
[¿¹Á¦ 1.10] 16Áø¼ö ABC.4A16À» 2Áø¼ö·Î º¯È¯Ç϶ó.
[¿¹Á¦ 1.11] 8Áø¼ö 789.1238À» 2Áø¼ö·Î º¯È¯Ç϶ó.
1.5.3 2Áø¼öÀÇ 10Áø¼ö·ÎÀÇ º¯È¯
ÀÓÀÇÀÇ
Áø¼ö¿¡¼ ÀÚ¸®ÀÇ À§Ä¡´Â ±× Áø¼öÀÇ x½Â Áï Áö¼ö½ÂÀ» ³ªÅ¸³½´Ù. ±×¸®°í ±× ÀÚ¸®À§Ä¡ÀÇ
°ª
±×ÀÚü´Â °¢ ÀÚ¸®ÀÇ À§Ä¡°ª°ú °öÇÒ °ªÀÌ µÈ´Ù. ÀÌ·¸°Ô ÇÏ¿© ±¸ÇÑ °¢ Ç×ÀÇ
°ªÀ» ´õÇØ°¡¸é ÇØ´ç
Áø¼öÀÇ 10Áø¼ö °ªÀÌ µÈ´Ù.
1.5.4 ¹Ýº¹ÀûÀÎ ³ª´°¼À¿¡ ÀÇÇÑ Áø¼öº¯È¯
Áø¼ö
º¯È¯Àº ÀÚ¸´¼ö °³³ä¿¡ ÀÇÇØ º¯È¯ÀÌ °¡´ÉÇÏÁö¸¸, º¸´Ù °£°áÇÑ ¹æ¹ýÀ¸·Î ¹Ýº¹ÀûÀÎ
³ª´°¼ÀÀ̶ó°í ÇÏ´Â ¾Ë°í¸®ÁòÀ» ÀÌ¿ëÇÔÀ¸·Î °¡´ÉÇÏ´Ù. ÀÌ ¹æ¹ýÀÇ Áø¼öº¯È¯Àº
º¯È¯ÇÏ·Á°í
ÇÏ´Â ¼ö NÀ» »õ·Î¿î Áø¼ö r·Î ³ª´©±â ÇÏ´Â °úÁ¤À» ¹Ýº¹ÇÏ¿© ±¸ÇÑ´Ù. ÀÌ ¹Ýº¹°úÁ¤ÀÇ
°¢ ³ª´°¼À
¿¡¼ ¾ò¾îÁö´Â ³ª¸ÓÁö´Â »õ·Î¿î Áø¼öÀÇ ÇϳªÀÇ ÀÚ¸´¼ö°¡ µÈ´Ù. ÀÌ °úÁ¤Àº MSB°¡
¾ò¾îÁú
¶§±îÁö °è¼Ó ¹Ýº¹µÈ´Ù. MSB´Â Á¦ÀÏ ÀÀÚ¸® ¼öÀÌ°í LSB´Â Á¦ÀÏ ¾Æ·§ÀÚ¸® ¼öÀÌ´Ù
[¿¹Á¦ 1.12] 10Áø¼ö 12010À» 2Áø¼ö·Î º¯È¯Ç϶ó.
120 / 2 = 60 -> 0 (LSB)
60 / 2 = 30 -> 0
30 / 2 = 15 -> 0
15 / 2 = 7 -> 1
7 / 2 = 3 -> 1
3 / 2 = 1 -> 1
1 / 2 = 0 -> 1
µû¶ó¼ 1111000 ÀÌ µÈ´Ù.
1.6 2Áø ÄÚµå
ÄÚµå : ¾î¶°ÇÑ Àǹ̸¦ °¡Áö´Â ÇϳªÀÇ ±âÈ£, ±âÈ£µéÀÇ ±×·ì
2Áø
ºÎÈ£È 10Áø¼ö(BCD: Binary Coded Decimal)´Â 10Áø¼ö¸¦ 2Áø¼ö·Î Ç¥±âÇϴµ¥
»ç¿ëÇϸç
½Ã°¢Àû Ç¥½ÃÀåÄ¡ÀÇ ±¸µ¿¿¡ Æí¸®ÇÏ´Ù.
1.6.1 2Áø ºÎÈ£È 10Áø¼ö(BCD)
»ç¶÷°ú µðÁöÅÐ ½Ã½ºÅÛ¿¡¼·Î °ü·ÃµÈ ÀÀ¿ë => ºÎÈ£ÈµÈ 2ÁøÁ¤º¸ ÇÊ¿ä => ÇϳªÀÇ
10Áø¼ö¸¦
Ç¥½ÃÇϱâ À§ÇØ 4ÀÚ¸®ÀÇ 2Áø¼ö(4ºñÆ®)±×·ìÀ¸·Î µÈ ÄÚµå(BCD) »ç¿ë. °³°³ÀÇ 10Áø¼ö¸¦
ÇϳªÀÇ
4ºñÆ® 2Áø ÄÚµå·Î º¯È¯µÇ±â ¶§¹®¿¡ ¿©·¯ ÀÚ¸®¸¦ °¡Áø 10Áø¼öµéÀº ¹Ù·Î BCD·Î
Ç¥ÇöµÇ´Â
¼ö·Î ºÎÈ£ÈÇÒ ¼ö ÀÖ´Ù.
---------------------- Áï 2ÁøÈ 10Áø¼ö(BCD)´Â
0 ¿¡¼ 9 ±îÁöÀÇ 10Áø¼ö °¢°¢¸¦
10Áø¼ö | 2Áø¼ö
4ºñÆ®ÀÇ 2Áø¼ö·Î Ç¥ÇöÇÏ´Â ¹æ½ÄÀ» ÀǹÌÇÑ´Ù.
----------------------
0
0000
----------------------
1
0001
----------------------
2
0010
----------------------
3
0011
----------------------
4
0100
----------------------
5
0101
----------------------
6
0110
----------------------
7
0111
----------------------
8
1000
----------------------
9
1001
----------------------
[¿¹Á¦ 1.13] 1987.510À» BCD ÄÚµå·Î º¯È¯Ç϶ó.