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# CH4 - Applications of BOOLEAN ALGEBRA Hasan Zidan Hasan...

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pplications of BOOLEAN Applications of BOOLEAN ALGEBRA asan Zidan Hasan Zidan Department of Electrical Engineering UST AUST 1

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Combinational logic One or more digital signal inputs One or more digital signal outputs Outputs are only functions of current input l (id l) l l i ti d l values (ideal) plus logic propagation delays Combinational Logic I 1 O 1 I m O n 2
Combinational logic Combinational logic has no memory. Outputs are only function of current input othing is known about past events Nothing is known about past events Repeating inputs always gives the same output sequence Sequential logic ( covered later ) Does have memory. Repeating inputs can result in an entirely different output Three steps in designing a single-output combinational switching network: Find a switching function which specifies the desired behavior of the network. Simplify the algebraic expression for the function. ealize the function using available logic elements (gates) Realize the function using available logic elements (gates) 3

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Combinational logic EX. Sentence Representation Equation Representation Z = The alarm will ring iff A = the alarm switch is on and = e door is ot osed r Z = AB + CD B the door is not closed or C = it is after 6 pm and D = the window is not closed. chematic A B D Z Schematic Representation C 4
Design using TRUTH Table Ex.: BC represents a it binary number e g 11 01 ABC represents a 3-bit binary number e.g. 011 = 3, 101 = 5 Output F is 1 if ABC >= 011 and is 0 if ABC < 011 A B C F 0 0 0 0 0 0 1 0 The ‘ 1 ’s represent F(A,B,C). 0 1 0 0 0 1 1 1 00 The ‘ 0 ’s represent F (A,B,C) 1 0 0 1 1 0 1 1 1 1 0 1 5 1 1 1 1

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EX. Cont’d: TRUTH TABLE TO SOP Can write SOP form of equation directly from truth table. F(A,B,C) = A’BC + AB’C’ + AB’C + ABC’ + ABC A B C F 0 0 0 0 01 0 = A’BC + AB’ + AB A’BC + A = A + BC 0 0 1 0 0 1 0 0 0 1 1 1 A BC = A BC + A = A + BC B 1 0 0 1 1 0 1 1 1 1 0 1 AB C AB C BC F C A 1 1 1 1 ABC ABC Note that each term in F has ALL variables present. If a 6 product term has ALL variables present, it is a MINTERM .
TRUTH Table POS FORM To get POS form of F, write SOP form of F , then use DeMorgan’s Law.

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CH4 - Applications of BOOLEAN ALGEBRA Hasan Zidan Hasan...

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