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PEPPERDINE COSC 425 - Combinational Circuits

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ChapterCombinationalCircuits100LFURFRGHOHYHO/RJLF JDWHOHYHO(OHFWURQLF GHYLFHOHYHO3K\VLFVOHYHO²Figure 10.1Combinational circuit•The output depends only on the inputDEF[\,Q 2XWFigure 10.2Methods to describe a combinational circuit•Truth table•Boolean algebraic expression•Logic diagramTruth table•Lists the output for every combination of the inputb00110011c01010101a00001111y0001100001010000xFigure 10.3a0000000011111111b0000111100001111c0011001100110011d0101010101010101y00001100000011000000010100000101xFigure 10.4Boolean algebra•Three basic operations‣Binary OR +‣Binary AND •‣Unary Complement ´Ten properties of boolean algebra•Commutative•Associative•Distributive•Identity•ComplementCommutativeCOMPUTER SYSTEMS CHAPTER 10x + y = y + x(1)x · y = y · x(2)(x + y) + z = x + (y + z)(3)(x · y) · z = x · (y · z)(4)x + (y · z) = (x + y) · (x + z)(5)x · (y + z) = (x · y) + (x · z)(6)x + 0 = x(7)x · 1 = x(8)x + (x�) = 1(9)x · (x�) = 0(10)x + y · z = (x + y) · (x + z)(11)x · (y + z) = x · y + x · z(12)x + x�= 1(13)x · x�= 0(14)(x + y) + z(15)x + y + z(16)x + x = x(17)x · x = x(18)x + 1 = 1(19)x · 0 = 0(20)x + x · y = x(21)x · (x + y) = x(22)x · y + x�· z + y · z = x · y + x�· z(23)(x + y) · (x�+ z) · (y + z) = (x + y) · (x�+ z)(24)(a · b�) = a�+ b�(25)(a + b)�= a�· b�(26)(x�)�= x(27)1�= 0(28)0�= 1(29)1AssociativeCOMPUTER SYSTEMS CHAPTER 10x + y = y + x(1)x · y = y · x(2)(x + y) + z = x + (y + z)(3)(x · y) · z = x · (y · z)(4)x + (y · z) = (x + y) · (x + z)(5)x · (y + z) = (x · y) + (x · z)(6)x + 0 = x(7)x · 1 = x(8)x + (x�) = 1(9)x · (x�) = 0(10)x + y · z = (x + y) · (x + z)(11)x · (y + z) = x · y + x · z(12)x + x�= 1(13)x · x�= 0(14)(x + y) + z(15)x + y + z(16)x + x = x(17)x · x = x(18)x + 1 = 1(19)x · 0 = 0(20)x + x · y = x(21)x · (x + y) = x(22)x · y + x�· z + y · z = x · y + x�· z(23)(x + y) · (x�+ z) · (y + z) = (x + y) · (x�+ z)(24)(a · b�) = a�+ b�(25)(a + b)�= a�· b�(26)(x�)�= x(27)1�= 0(28)0�= 1(29)1DistributiveCOMPUTER SYSTEMS CHAPTER 10x + y = y + x(1)x · y = y · x(2)(x + y) + z = x + (y + z)(3)(x · y) · z = x · (y · z)(4)x + (y · z) = (x + y) · (x + z)(5)x · (y + z) = (x · y) + (x · z)(6)x + 0 = x(7)x · 1 = x(8)x + (x�) = 1(9)x · (x�) = 0(10)x + y · z = (x + y) · (x + z)(11)x · (y + z) = x · y + x · z(12)x + x�= 1(13)x · x�= 0(14)(x + y) + z(15)x + y + z(16)x + x = x(17)x · x = x(18)x + 1 = 1(19)x · 0 = 0(20)x + x · y = x(21)x · (x + y) = x(22)x · y + x�· z + y · z = x · y + x�· z(23)(x + y) · (x�+ z) · (y + z) = (x + y) · (x�+ z)(24)(a · b�) = a�+ b�(25)(a + b)�= a�· b�(26)(x�)�= x(27)1�= 0(28)0�= 1(29)1IdentityCOMPUTER SYSTEMS CHAPTER 10x + y = y + x(1)x · y = y · x(2)(x + y) + z = x + (y + z)(3)(x · y) · z = x · (y · z)(4)x + (y · z) = (x + y) · (x + z)(5)x · (y + z) = (x · y) + (x · z)(6)x + 0 = x(7)x · 1 = x(8)x + (x�) = 1(9)x · (x�) = 0(10)x + y · z = (x + y) · (x + z)(11)x · (y + z) = x · y + x · z(12)x + x�= 1(13)x · x�= 0(14)(x + y) + z(15)x + y + z(16)x + x = x(17)x · x = x(18)x + 1 = 1(19)x · 0 = 0(20)x + x · y = x(21)x · (x + y) = x(22)x · y + x�· z + y · z = x · y + x�· z(23)(x + y) · (x�+ z) · (y + z) = (x + y) · (x�+ z)(24)(a · b�) = a�+ b�(25)(a + b)�= a�· b�(26)(x�)�= x(27)1�= 0(28)0�= 1(29)1ComplementCOMPUTER SYSTEMS CHAPTER 10x + y = y + x(1)x · y = y · x(2)(x + y) + z = x + (y + z)(3)(x · y) · z = x · (y · z)(4)x + (y · z) = (x + y) · (x + z)(5)x · (y + z) = (x · y) + (x · z)(6)x + 0 = x(7)x · 1 = x(8)x + (x�) = 1(9)x · (x�) = 0(10)x + y · z = (x + y) · (x + z)(11)x · (y + z) = x · y + x · z(12)x + x�= 1(13)x · x�= 0(14)(x + y) + z(15)x + y + z(16)x + x = x(17)x · x = x(18)x + 1 = 1(19)x · 0 = 0(20)x + x · y = x(21)x · (x + y) = x(22)x · y + x�· z + y · z = x · y + x�· z(23)(x + y) · (x�+ z) · (y + z) = (x + y) · (x�+ z)(24)(a · b�) = a�+ b�(25)(a + b)�= a�· b�(26)(x�)�= x(27)1�= 0(28)0�= 1(29)1PrecedenceHighestLowestOperatorComplementANDORFigure 10.5DistributiveCOMPUTER SYSTEMS CHAPTER 10x + y = y + x(1)x · y = y · x(2)(x + y) + z = x + (y + z)(3)(x · y) · z = x · (y · z)(4)x + (y · z) = (x + y) · (x + z)(5)x · (y + z) = (x · y) + (x · z)(6)x + 0 = x(7)x · 1 = x(8)x + (x�) = 1(9)x · (x�) = 0(10)x + y · z = (x + y) · (x + z)(11)x · (y + z) = x · y + x · z(12)x + x�= 1(13)x · x�= 0(14)(x + y) + z(15)x + y + z(16)x + x = x(17)x · x = x(18)x + 1 = 1(19)x · 0 = 0(20)x + x · y = x(21)x · (x + y) = x(22)x · y + x�· z + y · z = x · y + x�· z(23)(x + y) · (x�+ z) · (y + z) = (x + y) · (x�+ z)(24)(a · b�) = a�+ b�(25)(a + b)�= a�· b�(26)(x�)�= x(27)1�= 0(28)0�= 1(29)1ComplementCOMPUTER SYSTEMS CHAPTER 10x + y = y + x(1)x · y = y · x(2)(x + y) + z = x + (y + z)(3)(x · y) · z = x · (y · z)(4)x + (y · z) = (x + y) …


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