Digital Logic Circuits Lecture 10 Combinational Logic 1
Digital Logic Circuits Lecture 10 Combinational Logic (1) Ph. D. Eng. Ousama Bahbouh 1
CONTENTS 1. Combinational Circuits 2. Analysis Procedure 3. Design Procedure 4. Binary Adder - Subtractor 5. Decimal Adder 6. Binary Multiplier 7. Magnitude Comparator Dr. Eng. O. Bahbouh 2
: ANALYSIS PROCEDURE ﺇﺟﺮﺍﺋﻴﺔ ﺍﻟﺘﺤﻠﻴﻞ -2 A B C T 1 A B A C B C T 3 : ﺍﻟﺤﻞ F 1 T 2 T 6 F'2 F 2 T 4 T 5 Dr. Eng. O. Bahbouh 8
: ANALYSIS PROCEDURE ﺇﺟﺮﺍﺋﻴﺔ ﺍﻟﺘﺤﻠﻴﻞ -2 A B C T 1 A B A C B C T 3 : ﺍﻟﺤﻞ F 1 T 2 T 6 F'2 T 4 T 5 F 2 Dr. Eng. O. Bahbouh T 1= ABC T 2= A+B+C T 3= AB T 4= AC T 5= BC 9
: ANALYSIS PROCEDURE ﺇﺟﺮﺍﺋﻴﺔ ﺍﻟﺘﺤﻠﻴﻞ -2 A B C A B A C B C : ﺍﻟﺤﻞ T 1 F 1 T 2 T 6 F'2 T 3 T 4 T 5 F 2 Dr. Eng. O. Bahbouh T 3= AB T 4= AC T 5= BC F 2= T 3 +T 4 +T 5 F 2= AB + AC + BC 10
: ANALYSIS PROCEDURE ﺇﺟﺮﺍﺋﻴﺔ ﺍﻟﺘﺤﻠﻴﻞ -2 A B C A B A C B C : ﺍﻟﺤﻞ T 1 F 1 T 2 T 6 F'2 T 3 T 4 T 5 F 2 T 6= T 2 F'2 T 6= (A+B+C)(AB + AC + BC)' T 6= (A+B+C)(AB)' (AC)' (BC)' T 6= (A+B+C)(A'+B') (A'+C')(B'+C') Dr. Eng. O. Bahbouh 11
: ANALYSIS PROCEDURE ﺇﺟﺮﺍﺋﻴﺔ ﺍﻟﺘﺤﻠﻴﻞ -2 T 6 = (A+B+C)(A'+B') (A'+C')(B'+C') T 6 T 6 T 6 : ﺍﻟﺤﻞ = [(A+B+C)A'+(A+B+C)B'] (A'+C')(B'+C') = [(AA'+BA'+CA') +(AB'+BB'+CB')] (A'+C')(B'+C') = [BA'+CA'+AB'+CB'] [(A'+C')(B'+C')] = [BA'+CA'+AB'+CB'] [(A'B'+C'B')+(A'C'+C'C')] = [BA'+CA'+AB'+CB'] [A'B'+C'B'+A'C' +C'] = [BA'+CA'+AB'+CB'] [A'B+C'(B'+A'+1)] Dr. Eng. O. Bahbouh 12
: ANALYSIS PROCEDURE ﺇﺟﺮﺍﺋﻴﺔ ﺍﻟﺘﺤﻠﻴﻞ -2 T 6 = [BA'+CA'+AB'+CB'] [A'B+C'] : ﺍﻟﺤﻞ T 6 = BA'A'B'+BA'C'+CA'A'B'+CA'C'+AB'A'B'+AB'C'+ CB'A'B'+CB'C' T 6 = 0+BA'C'+CA'B'+0+0+AB'C'+CB'A'+0 T 6 = BA'C'+CA'B'+AB'C'+CB'A' T 6 = BA'C'+CA'B'+AB' C'= A'BC'+A'B'C+AB'C' Dr. Eng. O. Bahbouh 13
: ANALYSIS PROCEDURE ﺇﺟﺮﺍﺋﻴﺔ ﺍﻟﺘﺤﻠﻴﻞ -2 A B C T 1 A B A C B C T 3 : ﺍﻟﺤﻞ F 1 T 2 T 6 F'2 T 4 T 5 F 2 F 1= T 1+T 6 F 1= ABC+A'BC'+A'B'C+AB'C' Dr. Eng. O. Bahbouh 14
: DESIGN PROCEDURE ﺇﺟﺮﺍﺋﻴﺔ ﺍﻟﺘﺼﻤﻴﻢ -3 CD AB : ﺍﻟﺤﻞ 00 01 11 10 1 1 1 00 01 11 X X 10 1 1 X X w = A + BC + BD Dr. Eng. O. Bahbouh 20
: DESIGN PROCEDURE ﺇﺟﺮﺍﺋﻴﺔ ﺍﻟﺘﺼﻤﻴﻢ -3 CD AB : ﺍﻟﺤﻞ 00 00 01 1 11 X 10 01 11 10 1 1 1 X X X 1 X X x = B'C + B'D + BC'D' Dr. Eng. O. Bahbouh 21
: DESIGN PROCEDURE ﺇﺟﺮﺍﺋﻴﺔ ﺍﻟﺘﺼﻤﻴﻢ -3 CD AB : ﺍﻟﺤﻞ 00 01 11 00 1 1 01 1 1 11 X 10 X X y = CD + C'D' Dr. Eng. O. Bahbouh 22
: DESIGN PROCEDURE ﺇﺟﺮﺍﺋﻴﺔ ﺍﻟﺘﺼﻤﻴﻢ -3 CD AB : ﺍﻟﺤﻞ 00 01 11 10 00 1 1 01 1 1 11 X 10 1 X X X z = D' Dr. Eng. O. Bahbouh 23
: DESIGN PROCEDURE ﺇﺟﺮﺍﺋﻴﺔ ﺍﻟﺘﺼﻤﻴﻢ -3 w : ﺍﻟﺤﻞ A B x C D (C+D)' C+D y CD z Dr. Eng. O. Bahbouh 25
BINARY ADDER – ﺍﻻﺛﻨﺎﻧﻲ x 0 0 1 1 y 0 1 c 0 0 0 1 S = x'y + xy' C = xy s 0 1 1 0 x y' ﺍﻟﺠﺎﻣﻊ – ﺍﻟﻄﺎﺭﺡ -4 : SUBTRACTOR : Half Adder ﻧﺼﻒ ﺍﻟﺠﺎﻣﻊ S x' y x y Dr. Eng. O. Bahbouh C 28
BINARY ADDER – ﺍﻻﺛﻨﺎﻧﻲ ﺍﻟﺠﺎﻣﻊ – ﺍﻟﻄﺎﺭﺡ -4 : SUBTRACTOR : Half Adder ﻧﺼﻒ ﺍﻟﺠﺎﻣﻊ x 0 0 1 1 y 0 1 c 0 0 0 1 s 0 1 1 0 x y S C S = x'y + xy' = x ⊕ y C = xy Dr. Eng. O. Bahbouh 29
BINARY ADDER – ﺍﻻﺛﻨﺎﻧﻲ x 0 0 1 1 y 0 0 1 1 z 0 1 0 1 c 0 0 0 1 1 1 s 0 1 1 0 0 1 ﺍﻟﺠﺎﻣﻊ – ﺍﻟﻄﺎﺭﺡ -4 : SUBTRACTOR : Full Adder ﺍﻟﺠﺎﻣﻊ ﺍﻟﻜﺎﻣﻞ yz x 00 0 1 01 11 1 1 10 1 1 S = x'y'z + x'yz' + xy'z' + xyz Dr. Eng. O. Bahbouh 30
BINARY ADDER – ﺍﻻﺛﻨﺎﻧﻲ x 0 0 1 1 y 0 0 1 1 z 0 1 0 1 c 0 0 0 1 1 1 s 0 1 1 0 0 1 ﺍﻟﺠﺎﻣﻊ – ﺍﻟﻄﺎﺭﺡ -4 : SUBTRACTOR : Full Adder ﺍﻟﺠﺎﻣﻊ ﺍﻟﻜﺎﻣﻞ yz x 00 01 0 1 Dr. Eng. O. Bahbouh 11 10 1 1 C = xy + xz + yz = xy + xy'z + x'yz 31
BINARY ADDER – ﺍﻻﺛﻨﺎﻧﻲ x half adder 1 ﺍﻟﺠﺎﻣﻊ – ﺍﻟﻄﺎﺭﺡ -4 : SUBTRACTOR : Full Adder ﺍﻟﺠﺎﻣﻊ ﺍﻟﻜﺎﻣﻞ half adder 2 y S C z S = z ⊕( x ⊕ y) C = xy + z(x ⊕ y) Dr. Eng. O. Bahbouh 35
BINARY ADDER – ﺍﻻﺛﻨﺎﻧﻲ B 3 A 3 FA C 4 S 3 B 2 A 2 C 3 FA B 1 C 2 S 2 Dr. Eng. O. Bahbouh ﺍﻟﺠﺎﻣﻊ – ﺍﻟﻄﺎﺭﺡ -4 : SUBTRACTOR Binary ﺍﻻﺛﻨﺎﻧﻲ ﺍﻟﺠﺎﻣﻊ A 1 B 0 A 0 : Adder FA S 1 C 1 FA C 0 S 0 36
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