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Transcript of Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010....

Page 1: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� *�× � �¿TÒ¼m¬�× à�N��ï�æ·�+ ¬.Uè

|��ù

Page 2: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� ��

�¿TÒ¼m¬�×� �7Ho�>�s�àÔ�Ð ½$í÷& 9 Ø�¦§4��Ér {9�§4�°úכܼ�Ð ���&ñH�d

� �½+Ë�r�Ð_� �¦2�¤��s���ÕªÏþ� � ÕªaË> ��� � �

� í�H"f�r�Ð

� ¦�\¹�èכ�©��$ ��f�� <�Ê�Ér � � �� �� �� ¦�\¹�èכ ��f��

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� �&³F�_� {9�§4�õ� õ���_� {9�§4�\� _��>r �#� ���&ñH�d

� �� � !" #

Page 3: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� $ ��

à�N���/�×� � ��t� ×�æ¹כô�Ç [O�>�>h¥Æ�

� >�8£x&h� [O�>� % (��ÉÓ'� �Ð� [O�>� % ��¾Ód�� [O�>�

� >�8£x&h� [O�>�

� &' () ��H �Ð:�x úÑþ�ëß�>h_� >�s�àÔ�Ð ½$íH�d

� 4�¤ú��<Êܼ�Ð ô�Ç���\� [O�>�½+Éú \O�6£§ � �* +* � � �, � �-, .0/ �1 ~½ÓZO� ��6 x

� ì�r½+É�)a ����Ér �y���¦ �2 - �� s����¦ ÂÒ2£§ 3

� >�8£x&h� [O�>� � �54 ÕªaË> �� 6 % �� � �

� l��:r �¦2�¤ �7 1* 8* 9* + � � 2 - �� �

: �7Ho��r�Ð_� þj�èéß�0A % l� ñëß� ��6 x %; �< � 8 � 9* � \O�6£§

: �= �?> @> A >�s�àÔ

� �� � !" #

Page 4: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� � ��

à�N���/�× BDC EF GIH J K

� p�o�&ñ_��)a �¦2�¤ �7 1 �� �L , �� �2 - �� �

: l��:r�¦2�¤ �Ð�� 4�¤ú� % l� ñ ��6 x %; � < � 8 � 9* � \O�6£§

: �= �?M NO >�s�àÔ

� � 2 - �� _� F���6 x � 1lx{9�ô�Ç � 2 - �� \� @/ �#� ô�Ç���ëß� [O�>� ��¦ �� Qt���H F���6 x

� l�0px �¦2�¤ � �/ , � 9* -, � 2 � 2 - �� �

: p�o�&ñ_�÷&�¦ F���6 x��0px ��¦ n�t�_O� [O�>�\�"f V,�o� ��6 x÷&��H �¦2�¤

: P () úï�r_� [O�>�r� ��ÅÒ ��6 xH�d

: Q @ A 2* � 1 � 1 R �Ð t�"é¶H�d

� (��ÉÓ'� �Ð� [O�>�

� 4�¤ú�ô�Ç |9�&h��r�Ð [O�>�r� Q @ A � Q - 8 7 / 9 � 1 � @* � �� A �;* S, � s� \O�ܼ��� [O�>���Ô�¦��

� ( � < � 8 � 9* � �� 7 9/ 1 �

: �¦2�¤�¦ Õªo��¦ >�8£xZ>� �©� ñ�������¦ ��0px �>� �<Ê

: l��:r�¦2�¤ x9� l�0px�¦2�¤ úï�r_�2* � 1 � 1 R �� ]j/BNH�d

� �� � !" #

Page 5: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� T ��

à�N���/�× BDC EF GIH J K

� �7Ho� r�ÓýtYUs�'� �' - S* � ;* 8 / 2 � 9- 1 �

: [O�>��)a �r�Ð_� ���7£x�¦ 0A �#� �r�Ð\� r�çß�Z>��Ð {9�§4�x9� Ø�¦§4��¦ Òqt$í

� �7Ho� ½+Ë$í �' - S* � ; R, 9< �;* ; �

: �¦2�¤_� l�Õüt�)a "î[j"f\�¦ s�6 x �#� ��1lx �7Ho� ½�&³

: "î[j l�Õüt~½ÓZO�

U ���o�³ð

U �×¼J?#Q l�Õüt���#Q �?V A' � V � 1 �W � 1 � A �; � 1* 7 9* -, ' �, S/ � S � � ��6 x �

: ��1lx}9� C�u�ü< ��ĺh�A �½\�_�K� �©� ñ������÷&�¦ |9�&h��r�Ð C������t� ½$í

: [O�>� V A' l�Õüt\�"f |9�&h��r�Ð [O�>���t� ��1lx&h�ܼ�Ð ½$í½+Éú e��6£§

� ��¾Ód�� � 9- 7 � -W , � [O�>�

� �H �¦2�¤�¦ ����Ér �¦2�¤Ü¼�Ð ¹ô�Çכ��9 ëß��pu ��¾º#Q ½�&³

� ���FKd�� �©��¾Ód�� � � - 9 9- 8 / 7 � [O�>��� ��:ÉM+½¹כ��9 e��6£§

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Page 6: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� X ��

&P��7� â��� �½+Ë�r�Ð_� ì�r$3�

� �r�Ð�� ú'�� ���H l�0px�¦ ���&ñ

� �7Ho��\�¦ s�6 x �#� �r�Ð_� l�0px[O�"îõ� �<Êa� ÂÒÖ�¦�<Êú�� ���o�³ð\�¦ ]jr�

� 7£x"î Y l� l�Õüt�)a [O�"îõ� ì�r$3��)a l�0pxs� {9�u� ���H�� �����

� ì�r$3� ~½ÓZO�

: ÂÒÖ�¦Ãºd��s��� ���o�³ð\�¦ ú���\O�s��� �7Ho� r�ÓýtYUs�����¦ ��6 x �#� ì�r$3�

� ì�r$3� ]X��

� �½+Ë�r�Ð�����\�¦ SX����

: � � �� � � �� s��� l�%3����� \O���Ht� SX����

: ÂÒÖ�¦�<Êú�� ���o�³ð\�¦ ½�<Ê

: �r�Ð1lx����¦ K�$3�

� �� � !" #

Page 7: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� Z ��

&P��7� � BDC EF GIH J K

� ÂÒÖ�¦�<Êú_� Ä»�

� Ä»� õ�&ñ

� 3 {9�§4����ú ü< �Ðú\�@/ô�Ç Ø�¦§4�\� e��_�_� ÂÒ ñ ³ðr� Êê Ø�¦§4��<Êú\�¦ ½�<Ê

6 3 {9�§4����úü< ÂÒ ñ\� @/ô�Ç Ø�¦§4�\� e��_�_� ÂÒ ñ ³ðr�Êê Ø�¦§4��<Êú\�¦ ½�<Ê

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� \V � 4 ÕªaË> �� [

� ���o�³ð_� Ä»�

� �7Ho���ÐÂÒ'� Ä»�

: õ�&ñ

� 3 {9�§4�_� Ì�ú ���&ñ �]\ >h_� {9�§4�\� @/K� ^ \�"f _a` b c >h_� 6 ���ú l�{9� �

6 3 y�� �¦2�¤Ø�¦§4�\� e��_�_� l� ñ\�¦ ·¡­#� ���_� Ø�¦§4��¦ ����� �¦2�¤Ü¼�Ð ì�ro�

� 3 {9�§4����úëß�ܼ�Ð ���&ñ÷&��H �¦2�¤\� @/ �#� ���o�³ð\�¦ ½�<Ê

[ 3 ���H Ø�¦§4�\� @/ �#� ½ �#� |9�M:��t� ìøÍ4�¤

: \V � 4 ÕªaË> �� d � s���� ��íß�l� � � ���o�³ð � ³ð ��� � �

� �� � !" #

Page 8: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� e ��

&P��7� � BDC EF GIH J K

� �7Ho� r�ÓýtYUs����

� W1àÔ o�Û¼àÔ �, � 9 2* ; 9 � Y r�ÓýtYUs�'��� {9��¦Ãº e����H +þAI��Ð l�Õüt�)a �r�Ð

� ( � < � 8 � 9* � �� 7 9/ 1 � 9- - 2 Y �7Ho��\�¦ Õªwn=ú e��>� ���H �½

� 4 ÕªaË> �� f Y &* �W A 1 �W �Ð Õª�2;; � < � 8 � 9* �

� 4 ÕªaË> �� g Y &* �W h 1 � � � \� _�K� Òqt$í�)a ��+þA

� �� � !" #

Page 9: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� ��

à�N�â��� [O�>� Y ë�H]j � �7Ho���� ÂÒÖ�¦�<Êú

� õ�&ñ

� 3 ¹ô�Çכ��9 {9�Ø�¦§4� Ì�ú\�¦ ���&ñ ��¦ l� ñ½+É{©�

6 3 ���o�³ð\�¦ ���$í

� 3 çß�|ÄÌ�o�)a ÂÒÖ�¦�<Êú\�¦ %3�6£§

[ 3 �7Ho��\�¦ ÕªaË>

d 3 [O�>����õ�õ� ú���Ht� SX����

� \V]j �� �

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Page 10: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� i ��

�óÞ« >!a'a� ô�Ç �ï×¼\�¦ ���Ér �ï×¼�Ð ���8�

� \V � �� 6� j Q A � 9- � k = � �; ; � � �ï×¼ ��!Q'�

� ���o�³ð �54 ³ð �� 6 �

� çß�|ÄÌ�o�)a ÂÒÖ�¦�<Êú\�¦ %3�6£§ �54 ÕªaË> �� l �

� þj7áx&h�ܼ�Ð

mn ApoR n Q A q Qo A o n � Q r A �o

= n jo Q q jo A q j Qo A o n jo � Q q A �

q j Qo A o

W n @ q j Q q j A n @ q j � Q q A �

� �7Ho��\�¦ ÕªaË> Y 4 ÕªaË> �� � s

� \V � �� �� j Q A � 9- � g ; � S 8 �, 9 n��ï�8

� gt� ; � S 8 �, 9 ³ðr��©�u�

� 4 ÕªaË> ��� � � �

� ���o�³ð �54 ³ð �� � �

� �7Ho�çß�|ÄÌ�o �7 3 � � g �� �� � !" #

Page 11: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� u ��

g��óËÁ�H B Jv w E J v x y ¡�¡õe� K

� � � �- � � 1 Y �- � � � &ñ�Ð

� �, �- � � 1 Y &ñ�Ð � �- � �

� , �* 9 6 ��� �- � � r�

� {9�§4� Y,

� Ø�¦§4� Y _`

� �Ð:�x \ z _` � � �- � � 1 ��Ô�¦aË>

� \V � � z { � � �- � � 1

� ���o�³ð Y ³ð �� [

| } ~ � � � � � � � � � � � � � � � �

� � � � � � � � � � �

� � � � � � � � � � �

� � � � � � � � � � �

� � � � � � � � � � �

� � � � � � � � � � �

� � � � � � � � � � �

� � � � � � � � � � �

� � � � � � � � � � �

� �7Ho�[O�>� Y y��Ø�¦§4��Ér ���)3��½Ó\� K�{©� � 4 ÕªaË>

��� � 6 �

� �� � !" #

Page 12: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� ��

g��óËÁ�H B Jv w E J v x y ¡�¡õe� K BDC EF GIH J K

� �, � �2 � s� '�����)a� � �- � � 1

A’B’

A’B

AB’

AB

E

D0

D1

D2

D3

A

B

E

2x4Decoder

D0D1D2D3

� ���o�³ð x9� �7Ho�� �54 ÕªaË> �� � � �

� �� � !" #

Page 13: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� $ ��

g��óËÁ�H B Jv w E J v x y ¡�¡õe� K BDC EF GIH J K

� �, � � 2 � s� e����H 6 z [ � � �- � � 1 ��H � z [ � � 8 / 2 9* 7 2 �= � 1 %i�½+É�¦ �<ÊA’B’

A’B

AB’

AB

E

D0

D1

D2

D3

E1x4

Demulti-plexer

D0D1D2D3

A B

� �� � !" #

Page 14: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� � ��

g��óËÁ�H B Jv w E J v x y ¡�¡õe� K BDC EF GIH J K

� �, � � 2 � s� e����H 6 z [ � � �- � � 1 6 >h\�¦ s�6 x � z { � � �- � � 1 _� [O�>� �54 ÕªaË>

��� � [ �

� �� � !" #

Page 15: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� T ��

g��óËÁ�H B Jv w E J v x y ¡�¡õe� K BDC EF GIH J K

A

B

C

2x4Decoder

D0D1D2D3

2x4Decoder

D4D5D6D7

� �� � !" #

Page 16: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� X ��

g��óËÁ�HUc �+ø5� �¿TÒ¼Ðaµh� Ä©«Å�� � � �- � �1 _� Ø�¦§4��Ér ���)3��½Ó�¦ ³ðr� �l� M:ë�H\� e��_�_� �½+Ë�7Ho�\�¦ ½�&³½+É Ãº

e��6£§

� Ø�¦§4�s� � ��� ���)3��½Ó�¦ N O �Ð Óü�6£§Ü¼�Ð K����

� \V � �����íß�l�\�¦� � �- � � 1 ü< NO S � 9 � �Ð ½�&³ ���

� �����íß�l�

: ( �= % R % m �n � � � % 6 % [ % g �

: Q �= % R % m �n � � � % d % f % g �

� [O�>�ÕªaË> � 4 ÕªaË> ��� � d �

3x8Decoder

x

y

z

0123456

7

S

C

� �� � !" #

Page 17: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� Z ��

ê�>�óËÁ�H Bv F w E Jv x y ÉÙ¡õe� K

� �, �- � �1 ��H &ñ�Ð\�¦ �- � � �o ���H ����sכ 3

� &ñ�Ð��H #��Q>h_� ���ܼ�Ð [þt#Q� 9 y��y�� s õ� � _� °ú�כ¦ °ú���H��

� éß� 1lxr�\� ¿º >h_� ���s� � s� ÷&��H �âĺ��H \O����¦ ��&ñô�Ç�� 3

� _` >h_� {9�§4� ���\� @/ �#� \ �* 9 _� �- � � �� Ø�¦§4��)a��

� ��� s��©�_� {9�§4�s� � s� ÷&��H ��Érכ �¿º o�~��~��r�s��� 3

� ���o�³ð Y 4 ³ð �� d

� �� � !" #

Page 18: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� e ��

ê�>�óËÁ�H Bv F w E Jv x y ÉÙ¡õe� K BDC EF GIH J K

� � � � � � � � � � � � � � � � � � �

� s s s s s s s s s s

s � s s s s s s s s �

s s � s s s s s s � s

s s s � s s s s s � �

s s s s � s s s � s s

s s s s s � s s � s �

s s s s s s � s � � s

s s s s s s s � � � �

� �� � !" #

Page 19: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� ��

ê�>�óËÁ�H Bv F w E Jv x y ÉÙ¡õe� K BDC EF GIH J K

� �7Ho�� ½�&³D0D1D2D3D4D5D6D7

x=D4+D5+D6+D7

y=D2+D3+D6+D7

z=D1+D3+D5+D7

� ĺ��� í�H0A ����ï�8

� ¿º >h s��©�_� {9�§4�s� � s� ÷&%3��¦ M: Z�}�Ér ĺ��� í�H0A_� �¦ëß��כ �ï×¼�o�<Ê

� ���o�³ð �54 ³ð �� f �

� �7Ho�� �54 ÕªaË> �� � g �

� �� � !" #

Page 20: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� i ��

� �� G� ��� v �v x B � �� K

� #î§>= X<s�'� � f��§>=X<s�'�

� P  M �?¡ z c � _� [O�>�

4X1MUX

I0

Y

S1 S0

I1

I2

I3� ���o�³ð

¢ � ¢ � £

s s ¤ �

s � ¤ �

� s ¤ �

� � ¤ �

� �� � !" #

Page 21: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� $ u ��

� �� G� � � v �v x B � �� K BDC EF GIH J K

� �7Ho�� �54 ÕªaË> �� � { �

Y4x1

multiplexer

I0I1I2I3

S1 S0

S1’S0’

S1’S0

S1S0’

S1S0

I0

I1

I2

I3

Y

� �� � !" #

Page 22: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� $ ��

� �� G� � � v �v x B � �� K BDC EF GIH J K

� A � �- � � 1 \�¦ s�6 xô�Ç P  M _� ½�&³ � ���×þ� ����¦� � �- � � 1 �Ð @/u�½+É Ãº e���� �

I0

I1

I2

I3

Y

2x4Decoder

S1 S0

� ���5Åx>�s�àÔ\�¦ °ú���H [ � 9- � � 2* , � YO�w�e�¦�7�"f � 4 ÕªaË> ��� � l �

� [ >h_� 6� 9- � � 2* , � YO�w�e�¦�7�"f � 4 ÕªaË> ��� 6 s �

� �� � !" #

Page 23: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� $ $ ��

� �� �+ £� £� � P  M \� _�ô�Ç ÂÒÖ�¦�<Êú_� ½�&³

� \V � ��6£§ ���o�³ð\�¦ ½�&³ ���

���)3� @ j Q ¥

s s s s s

� s s � �

6 s � s s

� s � � �

[ � s s s

d � s � �

f � � s �

g � � � s

� �� � !" #

Page 24: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� $� ��

� � � �+ £� £� BDC EF GIH J K

� z��&³ ³ð\�¦ ëß�[þU

A’

A

I0 I1 I2 I3

0 1 2 3

4 5 6 7

0 1 A A’� ¡ z c P  M �Ð ½�&³

4X1MUX

0

F

B C

1

A

A’

� �� � !" #

Page 25: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� $ T ��

� � � �+ £� £� BDC EF GIH J K

� ¦ z c P  M �Ð ½�&³ ����

8X1MUX F

B CA

0

1

0

1

0

1

1

0

� \V � 4 ÕªaË> �� 6 � % ��� 6 6

� �� � !" #

Page 26: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� $ X ��

g�Þ�p��·øc"� B Jv § � � G� ��� v �v x K

� � � 8 / 2 9* 7 2 �= � 1 � A k P  M � Y f��§>=X<s�'� � #î§>=X<s�'�

� 8 / 2 9* 7 2 �= � 1 � P  M � Y #î§>=X<s�'� � f��§>=X<s�'�

MUX DEMUX

� �� � !" #

Page 27: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� $ Z ��

g�Þ�p��·øc"� B Jv § � � G� ��� v �v x K BDC EF GIH J K

� A k P  M � c z ¡ � _� [O�>�

1X4DEMUX

I

D0

D1

D2

D3

S1 S0

� {9�§4� &ñ�Ð\�¦ :£¤&ñ Ø�¦§4�ܼ�Ð �Ð?/l�0AK����×þ����s��9¹כ� Y _` {9�§4�\�@/ �#� \ >h_� ���×þ����

� ���o�³ð

¢ � ¢ � � � � � � � � �

s s s s s )

s � s s ) s

� s s ) s s

� � ) s s s� �� � !" #

Page 28: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� $ e ��

g�Þ�p��·øc"� B Jv § � � G� ��� v �v x K BDC EF GIH J K

� �7Ho��S1’S0’

S1’S0

S1S0’

S1S0

I

D0

D1

D2

D3

I1x4

Demulti-plexer

D0D1D2D3

S1 S0

� �� 9- � [ 2* , � n�YO�w�e�¦�7�"f �54 ÕªaË> �� 6 � �

� �� � !" #

Page 29: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� $ ��

¨ ë�> ��ñ5Ñe�� 6 �* 9 x9� � �* 9 ��íß�l�\�¦ [O�>��<Ê

� ¿º 7áxÀÓ_� ��íß�l�

� ìøÍ��íß�l� � V � 2 � @ � � �1 Y V @ � Y 6 �* 9 ��íß�l�

� �����íß�l� � ¥/ 2 2 @ � � � 1 Y ¥ @ � Y � �* 9 ��íß�l� � 6 �* 9 q � �* 9 �� 1 1 R

A

B

Sum

Carry Out Carry InHA

AB

Sum

Carry OutFA

� \V � [ �* 9 _� 6 ���úM %© \�¦ �8½+ÉM:

ª« ª¬ ª­ ª®

¯ « ¯ ¬ ¯ ­ ¯ ®

° ± « ± ¬ ± ­ ± ®² ² ² ² ² ² ² ² ² ² ² ² ² ² ²

³« ³¬ ³­ ³®

´µ ´µ ´µ ¶ µ

� �� � !" #

Page 30: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� $ i ��

¨ ë�> ��ñ5Ñe� BDC EF GIH J K

� ìøÍ��íß�l�_� [O�>�

� ���o�³ð\�¦ ���$í{9�§4� Ø�¦§4�

= R Q (

s s s s

s � s �

� s s �

� � � s

� çß�|ÄÌ�o�)a ÂÒÖ�¦�<Êú\�¦ %3�6£§

Q n = R

( n = o R q = Ro n �= o q Ro � �= q R �n �= o Ro q = R �o n = r R� �� � !" #

Page 31: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� � u ��

¨ ë�> ��ñ5Ñe� BDC EF GIH J K

� �7Ho��\�¦ ÕªaË>

xy

S

C

S C

0

1

xy

0 1

0

1

xy

0 1

1

1 1

S = x’y+xy’ = x y

C = xy

� �� � !" #

Page 32: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� � ��

¨ ë�> ��ñ5Ñe� BDC EF GIH J K

� �����íß�l�_� [O�>�

� ���o�³ð\�¦ ���$í{9�§4� Ø�¦§4�

= R m Q (

s s s s s

s s � s �

s � s s �

s � � � s

� s s s �

� s � � s

� � s � s

� � � � �

� çß�|ÄÌ�o�)a ÂÒÖ�¦�<Êú\�¦ %3�6£§

: ( \� @/ô�Ç �ØÔ� ë�s

0

1

xyz

00 01 11 10

1

1

1

1: ���²DG Y ( n = o Ro m q = o R mo q = Ro mo q = R mn m r �= r R �

: Q \� @/ô�Ç �ØÔ� ë�s

0

1

xyz

00 01 11 10

1

1 1

xz xy

1

yz

: ���²DG Y Q n = R q = m q R m n = Ro m q = o R m q = R n

m �= Ro q = o R � q = R

� �7Ho��\�¦ ÕªaË>

� �� � !" #

Page 33: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� � $ ��

¨ ë�> ��ñ5Ñe� BDC EF GIH J K

: ìøÍ��íß�l�\�¦ s�6 xô�Ç �����íß�l�_� ½�&³S = x’y’z + x’yz’ + xy’z’ + xyz = z (x y)

C = xy + xz + yz = xy’z + x’yz + xy = z(xy’ + x’y) + xy = z(x y) + xy

xy S

C

z

: �7Ho�� �54 ÕªaË> �� 6 f �

* ìøÍy��íß�l�ü< ���y��íß�l� 0Aü< °ú s� [O�>�½+É Ãº e���� 3

� 6 ��� o�e�¦H�o� ��íß�l� �54 ÕªaË> �� 6 g �

� �� � !" #

Page 34: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� � � ��

¨ ë�> ��ñ5Ñe� BDC EF GIH J K

� H�o� \V|� ��íß�l�

� 0Aü< °ú �Ér o�e�¦H�o� ��íß�l�\�"f ���íß�r�çß� Y Q d �� 1 1 R ���íß�r�çß�ܼ�Ð ô�Ç&ñH�d

� y�� q�àÔ\�"f �� 1 1 R \�¦ p�o� >�íß� �' - - � � � < �� � �� 1 1 R �

: � �� 1 1 R 7 1 - 7 � S � 9 � �?· * n @* r j*

: � �� 1 1 R S �, � 1 � 9- 1 �]¸ * n @* j* ���¦ &ñ ����

: �����íß�l���H

U (* n @* r j* r Q* n · * r Q*

U Q* q � n Q* � @* r j* � q @* j* n Q* · * q ¸ * ��H�d

: Õª�QÙ¼�Ð Q � s� ÅÒ#Qt����

U Q 6 n Q �· � q ¸ �

U Q � n Q 6· 6 q ¸ 6 n � Q �· � q ¸ � �· 6 q ¸ 6 n Q �· �· 6 q ¸ �· 6 q ¸ 6

U Q [ n Q �· � q ¸ � n Q �· �· 6· � q ¸ �· 6· � q ¸ 6· � q ¸ �

7£¤ �©�0AH�o�\�¦ Q � õ� ¿ºq�àÔ�Ð ���Ð ëß�[þt ú e���� 3

: ' - - � � � < �� � �� 1 1 R S �, � 1 � 9- 1 \�¦ s�6 xô�Ç [ q�àÔ �����íß�l� �54 ÕªaË> �� 6 { �� �� � !" #

Page 35: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� � T ��

¨ ë�> ��ñ5Ñe� ¹ ÇÔñ5Ñe�� ÂÒ ñ\�¦ °ú���H 6 ���ú �54 ³ð ��� l �

� ÂÒ ñ�o�)a ]X�@/°úכ ³ð�&³ �;* S, �� � 8 � S, * 9/ � � � Y ÂÒ ñü< ß¼l��Ð ³ð�&³

� ÂÒ ñ�o�)a �Ðú ³ð�&³ �;* S, �� � �- 8 7 2 � 8 �, 9 � Y ÂÒ ñü< �Ðú � 6£§Ãº{9��âĺ � �Ð ³ð�&³

� ��íß�� y��íß�l� �r�Ð �54 ÕªaË> ��� � s �

� ÂÒ ñ�o�)a 6 ��� ��íß�õ� y��íß� � \V]j �� { �

� �!Qe�¦�Ðĺ

� 6 >h_� \ q�àÔ_� ½+Ës� \ º c q�àÔ\�¦ �t�½+ÉM: µ1ÏÒqt

� ÂÒ ñ�o �%i��¦�âĺ��H þj�©�0Aq�àÔ�Ð H�o� ü< þj�©�0Aq�àÔ\�"f H�o�×�æ � _�Ì�ú�� f.Ëú{9�M: µ1ÏÒqt

� �!Qe�¦�Ðĺ ���Ø�¦�r�Ð � ÕªaË> ��� � � �

� 6 ��� Y�L!lrl�

� 6 ��� Y�L!lrl�_� �7Ho�� � 4 ÕªaË> �� � 6 �

� [ �* 9 z � �* 9 6 ��� Y�L!lrl� �54 ÕªaË> �� � � �

� �� � !" #

Page 36: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� � X ��

» ¼ ë�> ñ5Ñ�ä·¥o>ñ5Ñ� ¿º >h_� z�����ú\�¦ �8 ���H ��íß�l� Y l >h_� {9�§4� d >h_� Ø�¦§4�s� ¹כ��9

� �7Ho�[O�>�~½ÓZO�ܼ�Ð��H �-Áº 4�¤ú�

� ¿º >h_� [ �* 9 6 �����íß�l�\�¦ s�6 x

� ¿º >h_� ô�Ç��o� z�����ú @ % j \�¦ �8�<Ê

² ªÝî­ÝáªÁ ² ² ² ² ¬È­ÝáªÁ ² ² ²

ª½ ª½

µ µ¾ µ « µ ¬ µ ­

° ¿ ° ¿¾ ¿ « ¿ ¬ ¿ ­

² ² ² ² ² ² ² ² ² ² ² ² ² ² ² ²

ª½ ° ­ ³ ª½ ° ­ ³¾ ³« ³¬ ³­

� ¿º >h_� z�����ú\�¦ �8Ùþ¡�¦ M: þj@/ß¼l� Y l q l q � � �� 1 1 R �n � l

� �� � !" #

Page 37: Nˆ à– Š× m‹ TÒ… œ¿itsys.hansung.ac.kr/lec/dlogic/mylec/OLD2_version/chap3/... · 2010. 5. 12. · 4X1 MUX I0 Y S1 S0 I1 I2 I3 fl˙o˙‡ð ¢ £ s ¤ s ¤ s ¤ ¤ !

� �©� � �½+Ë�r�Ð [O�>� ��� �� � Z ��

» ¼ ë�> ñ5Ñ�ä·¥o>ñ5Ñ BDC EF GIH J K

� [O�>�~½ÓgË>

: ¿º >h_� z�����ú\�¦ �8ô�Ç

���õ��� l �Ð�� ���ܼ��� Õª@/�Ð Ø�¦§4� % �� 1 1 R \O�6£§

: ¿º >h_� z�����ú\�¦ �8ô�Ç

���õ��� l �Ð�� ß¼��� � s ���ú�Ð ��ÀDK Y f � s � � s � �¦�8�<Ê % �� 1 1 R e��6£§

: ���²DG �� 1 1 R �� e��ܼ���

s � � s �¦ �8�<Ê % \O�ܼ��� Õª@/�Ð Ø�¦§4�

: ���o�³ð\�"f �� 1 1 R ��µ1ÏÒqt ���H �|��¦ ½�<Ê

U Q* q � n À q Á { Á [ q

Á { Á 6

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4-bit binary adder Carryin

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Outputcarry

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S8 S4 S2 S1

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0

4-bit binary adder

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