Recitation3

Upcoming Schedule: 

Upcoming Schedule Today: Review for Midterm Thursday (1/22): 5pm to 7pm HKN review in the Greenwalt Student Development Center Room C (basement of the Creese Building) Monday (1/26): Midterm Exam I Labs due in Recitation (1/29, 1/30) Groups?? Tuesday (2/3): Homework #3 Next week office hours moved to Friday from 3:00-5:00

Midterm Review - What we have done so far….: 

Midterm Review - What we have done so far…. Numbers Binary, Oct, Hex Signed and Unsigned Conversion to/from any base Addition/Subtraction 2’s complement Combinational Logic AND, OR, NOT, XOR Laws and truth tables – Algebraic Simplification Proof Algebraic Perfect Induction (Truth Tables) Duality / DeMorgan’s

Midterm Review – What will it cover?: 

Midterm Review – What will it cover? Dr. Sethu’s Lectures Homework: Homeworks 1-2 Book: Chapter 1: All Sections Chapter 2: Sections 2.1-2.6 (except 2.5.5, 2.5.6 and 2.5.7) Chapter 3: Sections 3.1, 3.2, 3.4 Chapter 4: Section 4.1 (except subsection 4.1.6)

Numbers: 

Numbers Convert to any base: 19910 = ?9 Convert 32034 to binary without going through decimal How can we check our answer??

Review of 2’s complement: 

Review of 2’s complement Numbers must all be represented by the same number of bits (input and output #s!) The final carry is ignored Check for overflow if both numbers are positive or if both are negative 2’s Complement (8-bit) Addition & Subtraction: 119: 01110111 28: 00011100 28 – 119 = -119 – 28 =

Switching Algebra/Simplification: 

Switching Algebra/Simplification Mathematical notation to describe the operational properties of digital circuits How can we check this solution?? theorem dual (and  or, 0  1) name (T1) X + 0 = X X · 1 = X identity (T2) X + 1 = 1 X · 0 = 0 null elements (T3) X + X = X X · X = X idempotency (T4) (X’)’ = X (X’)’ = X involution (T5) X + X’ = 1 X · X’ = 0 complement (T6) X + Y = Y + X X · Y = Y · X commutativity (T7) (X + Y) + Z = X + (Y + Z) (X·Y) · Z = X· (Y·Z) associativity (T8) X·Y + X·Z = X·(Y + Z) (X + Y)·(X + Z) = X + Y·Z distributivity (T9) X + X·Y = X X·(X + Y) = X covering (T10) X·Y + X·Y’ = X (X + Y)·(X + Y’) = X combining (T13) (X · Y)’ = X’ + Y’ (X + Y)’ = X’ · Y’ DeMorgan’s

Simplification: 

Simplification

Duality and DeMorgan’s: 

Duality and DeMorgan’s Duality Replace all 0’s by 1’s, and vice versa Replace all • by +, and vice versa DeMorgan’s (find the inverse) Replace all • by +, and vice versa Complement each part

DeMorgan’s: 

DeMorgan’s Steps for DeMorgan’s AND  OR Complement each side Keep using DeMorgan’s until there is no complement of a gate Express function using all OR Express function using all AND