CH2 - BOOLEAN ALGEBRA Hasan zidan Department of Electrical...

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OOLEAN ALGEBRA BOOLEAN ALGEBRA asan dan Hasan zidan Department of Electrical Engineering UST AUST 1
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Introduction asic mathematics for the study of logic design is Basic mathematics for the study of logic design is Boolean Algebra by George Boole 1847 . asic laws of Boolean Algebra will be Basic laws of Boolean Algebra will be implemented as switching devices called logic gates. Networks of Logic gates allow us to manipulate digital signals Can perform numerical operations on digital signals such as addition, multiplication Can perform translations from one binary code to another. 2
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Boolean Variables, Functions oolean variable n take on two values | A Boolean variable can take on two values, 0 and 1 , T and F , H and L or ON, OFF . | Basic operations are NOT, AND , and OR | We can make more complicated Boolean unctions om the basic Boolean operations Functions from the basic Boolean operations 3
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NOT Operation The NOT operation (inverse, or complement operation) places a boolean value with its complement: replaces a boolean value with its complement: 0 = 1 1 = 0 Truth Table A is read as NOT Aor Complement A A Y 0 1 1 0 A A Inverter symbol NOT Y=F(A) = A boolean representation 4
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AND Operation The AND operation is a function of two variables (A, B) (A , B) = A boolean function representation F(A , B) A B When both A and B are 1 , then F is 1. 0 1 1 0 0 = 0 0 1 = 0 1 0 = 0 1 1 = 1 Truth Table witch Open ( A B Y 0 0 0 1 0 AND B Y = A B Switch Open (0) Switch Closed (1) 00 1 0 0 1 1 1 A = AB = rcuit closed 5 A B T AB 1 Æ circuit closed
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OR Operation OR operation is a function of min. two variables (A, B) F(A,B) = A + B boolean function representation when either A or B ‘1’, then F is ‘1’. 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 1 ruth Table A B Y 0 0 Truth Table 0 0 0 1 1 1 0 1 OR Y = A + B A B 6 1 1 1
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OR Operation ( CONT’D ) an view R peration as two switches in parallel: Can view OR operation as two switches in parallel: A Neither switch A or switch B is B closed, so circuit is open (0) A
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CH2 - BOOLEAN ALGEBRA Hasan zidan Department of Electrical...

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