Class Notes (835,428)
CSC258H1 (46)
Lecture

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Department
Computer Science
Course
CSC258H1
Professor
Steve Engels
Semester
Winter

Description
CIRCUIT CREATION o Ex. m 2 output (Y1) only goes high in the third line of truth table  Making logic with gates A B C D m 2 m 8 Y1 Y2 0 0 0 0 0 0 0 0 o Logic gates like the following allow us to create an output value, 0 0 0 1 0 0 0 0 based on two inputs 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1 0 1 0 0 0 0 o What do we do in the case of more complex circuits, with several 0 1 1 0 0 0 0 0 0 1 1 1 0 0 0 0 inputs and more than one output? 1 0 0 0 0 1 0 1  Circuit example 1 0 0 1 0 0 0 0 o The circuit on the right has 1 0 1 0 0 0 0 0 1 0 1 1 0 0 0 0 tree inputs (A, B and C) 1 1 0 0 0 0 0 0 and two outputs (X and Y) 1 1 0 1 0 0 0 0 1 1 1 0 0 0 0 0 o What logic is needed to set X high when all three 1 1 1 1 0 0 0 0 o When OR two minterms (m +m ), result is output (Y2) that goes inputs are high? 2 rd th high in both minterm cases (3 and 9 row) o What logic is needed to set o Two canonical forms of boolean expressions: Y high when the number of high inputs is odd?  Combinational Circuits  Sum-of-Minterms (SOM)  Since each minterm corresponds to a single high output o Small problmes can be solved easily in the truth table, the combined high outputs are a union of these minterms  Also known as: Sum-of-Products  Ex. Y = m + m + m + m 2 6 7 10 A B C D m 2 m 6 m7 m10 Y o Larger problems require a more systematic approach 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0  Ex. Given three inputs A, B, and C, make output Y high in the 0 0 1 0 1 0 0 0 1 case where all of the inputs are low, or when A and B are low 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 and C is high, or when A and C are low but B is high, or when A is low and B and C are high. 0 1 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1  Creating logic 0 1 1 1 0 0 1 0 1 o Basic steps 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0  1. Create truth tables 1 0 1 0 0 0 0 1
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