Designing Combinational Logic Circuits Unit 3 Designing Combinational Logic Circuits

Design of logic circuit is possible when the desired output level of the logic circuit is displayed in a truth table. From the truth table, the Boolean expression is derived and using Boolean algebra to simplify the expression.

Example 1 Circuit design Output X is only for the case where A = 0 & B = 1. A/An AND gate is used with inputs A & B, so that X = AB Circuit design

Example 2 Circuit design Output X is 1 when A = 0, B = 1 OR A = 1, B = 0 Circuit design

Example 3 Circuit design

General procedure for obtaining the output expression (SOP form) from a truth table: Write an AND term for each case in the table where the output is 1. Each AND term contains each input variable in either inverted or non-inverted form. If the variable is ‘0’ for that particular case in the table, it is inverted in the AND term. All the AND terms are then ORed together to produce the final expression for the output.

Exercises Design a logic circuit that has three inputs A, B and C and whose output will be high only when a majority of the input is high. Solution: Truth table Boolean Algebra X = ABC + ABC + ABC + ABC X = ABC + ABC + AB X = ABC + A(BC + B) A(C + B) X = ABC + AC + AB X = AC C(AB + A) C(B + A) + BC + AB

K Map AB + AC + BC Circuit Design AB AC = AB + AC + BC BC

Four logic signal lines A, B, C and D are used to represent a 4-bit binary number with A as MSB and D the LSB. The binary inputs are fed to a logic circuit that produces a HIGH output only when the binary number is greater than 01102 = 610. Design this circuit. Truth table Boolean Algebra X = ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD + ABCD X = ABC + ABC + ABC + ABC + ABC X = ABC + AB + AB X = ABC + A

K Map A + AC Circuit Design A = A + AC AC

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