Boolean AlgebraLogic Gate Karnaugh Map
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ºÎ¿ï´ë¼ö(Boolean Algebra)
³í¸®°ÔÀÌÆ®(Logic Gate)
Ä«¸£³ë¸Ê(Karnaugh Map)
2º¯¼ö, 3º¯¼ö, 4º¯¼ö Ä«¸£³ë¸Ê
°£¼ÒÈ ¹æ¹ý
¹®Á¦ Ç®ÀÌ
ºÎ¿ï ´ë¼ö(Boolean Algebra)
1854³â¿¡ George BooleÀÌ ±âº»ÀûÀÎ ¿ø¸®¸¦ ÁÖâ
2 Áø º¯¼ö¿Í ³í¸® µ¿ÀÛÀ» Ãë±ÞÇÏ´Â ÇÔ¼ö
º¯¼ö´Â ¡®0¡¯°ú ¡®1¡¯ÀÇ µÎ °ª Áß¿¡ Çϳª¸¦ °¡Áö¸ç º¯¼ö À̸§Àº ¿µ¹®ÀڷΠǥ½Ã
ºÎ¿ï ´ë¼ö(Boolean Algebra)
ºÎ¿ï ´ë¼öÀÇ ±âº» ³í¸® µ¿ÀÛ
³í¸® °ö(AND) : ¤ý
³í¸® ÇÕ(OR) : +
ºÎÁ¤ ºÎÁ¤(NOT) : ¡¯ ¶Ç´Â £þ
A B
A¤ýB
A + B
A¡¯
B¡¯
0 0
0
0
1
1
0 1
0
1
1
0
1 0
0
1
0
1
1 1
1
1
0
0
ºÎ¿ï ´ë¼ö(Boolean Algebra)
ºÎ¿ï ´ë¼öÀÇ ±âº» Á¤¸®
x + 0 = x
x¤ý1 = x
x + 1 = 1
x¤ý0 = 0
°¡¿ªÁ¤¸®
x + x¡¯ = 1
x¤ýx¡¯ = 0
µ¿ÀϹýÄ¢
x + x = x
x¤ýx = x
ºÎÁ¤ÀÇ ¹ýÄ¢
(x¡¯)¡¯ = x
±³È¯¹ýÄ¢
x + y = y + x
x¤ýy = y¤ýx
°áÇÕ¹ýÄ¢
x + (y + z) = (x + y) + z
x(yz) = (xy)z
ºÐ¹è¹ýÄ¢
x¤ý(y + z) = xy + xz
x + yz = (x + y)(x + z)
De Morgan Á¤¸®
(x + y)¡¯ = x¡¯y¡¯
(xy)¡¯ = x¡¯ + y¡¯
Èí¼ö¹ýÄ¢
x + xy ¡¦(»ý·«)
|
1
0
1
1
BC
A
00
01
11
10
0
1
1
1
1
1
F = AC¡¯ + BC
BC
AC¡¯
¹®Á¦ Ç®ÀÌ
1. ´ÙÀ½À» Boole´ë¼ö¸¦ ÀÌ¿ëÇÏ¿© °£·«ÈÇ϶ó.
¹®) ABC + A¡¯B + ABC¡¯
= AB(C+C¡¯) + A¡¯B
= AB + A¡¯B
= B(A + A¡¯)
= B
¹®Á¦ Ç®ÀÌ
2. F=A¡¯C¡¯+ABC+AC¡¯ ¸¦ Ä«¸£³ë¸ÊÀ» ÀÌ¿ëÇÏ¿© °£·«È(1)ÇÏ°í ±× °á°ú¸¦ ³í¸®µµ(2)·Î ³ªÅ¸³»½Ã¿À.
BC
A
00
01
11
10
0
1
1
1
1
1
1
C¡¯
AB
(1) F = C¡¯ + AB
¹®Á¦ Ç®ÀÌ
F = C¡¯ +AB
(2)
A
B
C
F