Gate-level Design: Full Adder  Truth table: Note: Z - carry in (to the current position) C - carry out (to the next position)  Using K-map, simplified.

Slides:

Advertisements

Similar presentations

Assignments The submission has to be by the end of this week Write your full name and the group number on the answer sheet.

Advertisements

Combinational Circuits. Analysis Diagram Designing Combinational Circuits In general we have to do following steps: 1. Problem description 2. Input/output.

التصميم المنطقي Second Course

CS2100 Computer Organisation Combinational Circuits (AY2014/5 Semester 2)

ECE 331 – Digital System Design Boolean Algebra (Lecture #3) The slides included herein were taken from the materials accompanying Fundamentals of Logic.

ECE 331 – Digital System Design

COMBINATIONAL LOGIC CIRCUITS C.L. x1 x2 xn Z Z = F (x1, x2, ……., Xn) F is a Binary Logic (BOOLEAN ) Function Knowing F Allows Straight Forward Direct Implementation.

Section 10.3 Logic Gates.

ECE 301 – Digital Electronics

CS 300 – Lecture 3 Intro to Computer Architecture / Assembly Language Digital Design.

Part 2: DESIGN CIRCUIT. LOGIC CIRCUIT DESIGN x y z F F = x + y’z x y z F Truth Table Boolean Function.

CS1104: Computer Organisation Lecture 6: Combinational Circuits Design Methods/Arithmetic Circuits

CS 105 Digital Logic Design

Lecture No. 14 Combinational Functional Devices svbitec.wordpress.com.

XOR, XNOR, and Binary Adders

22C:19 Discrete Math Boolean Algebra & Digital Logic Fall 2010 Sukumar Ghosh.

CHAPTER 2 Boolean Algebra

Morgan Kaufmann Publishers

Logic Design CS221 1 st Term combinational circuits Cairo University Faculty of Computers and Information.

Combinational Logic Chapter 4.

1 COMBINATIONAL LOGIC One or more digital signal inputs One or more digital signal outputs Outputs are only functions of current input values (ideal) plus.

Binary Addition Section 4.5. Binary Addition Example.

Boolean Algebra and Digital Circuits

Eng. Mohammed Timraz Electronics & Communication Engineer University of Palestine Faculty of Engineering and Urban planning Software Engineering Department.

Discrete Mathematics CS 2610 February 19, Logic Gates: the basic elements of circuits Electronic circuits consist of so-called gates connected.

F = ∑m(1,4,5,6,7) F = A’B’C+ (AB’C’+AB’C) + (ABC’+ABC) Use X’ + X = 1.

WEEK #10 FUNCTIONS OF COMBINATIONAL LOGIC (ADDERS)

Computer Organization 1 Logic Gates and Adders. Propositions –Venn Diagrams.

Chapter 10 (Part 2): Boolean Algebra  Logic Gates (10.3) (cont.)  Minimization of Circuits (10.4)

Boolean Logic and Circuits ELEC 311 Digital Logic and Circuits Dr. Ron Hayne Images Courtesy of Cengage Learning.

Venn Diagram – the visual aid in verifying theorems and properties 1 E.

Sneha.  A combinational circuit that performs the addition of two bits is called a half adder.  It has two inputs.  It has two outputs.

Computer Systems 1 Fundamentals of Computing Simplifying Boolean Expressions.

Boolean Algebra and Logic Gates CSE-1108 Ahsanullah University of Science and Technology (AUST)

Minimization Karnaugh Maps

Boolean Algebra & Logic Circuits Dr. Ahmed El-Bialy Dr. Sahar Fawzy.

Module 5.  In Module 3, you have learned the concept of Boolean Algebra which consists of binary variables and binary operator.  A binary variable x,

BOOLEAN ALGEBRA – Digital Circuit 1 Choopan Rattanapoka.

Chapter 3 Digital Logic Structures

Boolean Algebra ELEC 311 Digital Logic and Circuits Dr. Ron Hayne Images Courtesy of Cengage Learning.

Function Simplification. Outline  Function Simplification  Algebraic Simplification  Half Adder  Introduction to K-maps  Venn Diagrams.

1 Logic Gates CS 202, Spring 2008 Epp, sections 1.4 and 1.5.

LOGIC CIRCUITLOGIC CIRCUIT. Goal To understand how digital a computer can work, at the lowest level. To understand what is possible and the limitations.

UNIT 8 COMBINATIONAL CIRCUIT DESIGN AND SIMULATION USING GATES

Lecture No. 14 Combinational Functional Devices. Digital Logic &Design Dr. Waseem Ikram Lecture 14.

1 Review of Boolean algebra Not is a horizontal bar above the number –0 = 1 –1 = 0 Or is a plus –0+0 = 0 –0+1 = 1 –1+0 = 1 –1+1 = 1 And is multiplication.

Gunjeet Kaur Dronacharya Group of Institutions. Binary Adder-Subtractor A combinational circuit that performs the addition of two bits is called a half.

Combinational Circuits

Unit 2 Boolean Algebra.

CS2100 Computer Organisation

EXAMPLES- Simplifying Radicals part 2

CHAPTER 2 Boolean Algebra

CHAPTER 2 Boolean Algebra This chapter in the book includes:

Lecture 2-1 Boolean Algebra

Combinational Circuits

Computer Architecture CST 250

ENG6530 Reconfigurable Computing Systems

FIGURES FOR CHAPTER 2 BOOLEAN ALGEBRA

Gate-level Design: Full Adder

DIGITAL LOGIC CIRCUITS

Lecture 14: Boolean Algebra

Example Question: Consider the expressions: (a) F = XY + XY'

ECE 301 – Digital Electronics

Unit 5 COMBINATIONAL CIRCUITS-1

Adders and Subtractors

COMS 361 Computer Organization

DIGITAL ELECTRONICS B.SC FY

XOR Function Logic Symbol  Description  Truth Table 

Boolean Algebra and Gate Networks

Presentation transcript:

Gate-level Design: Full Adder  Truth table: Note: Z - carry in (to the current position) C - carry out (to the next position)  Using K-map, simplified SOP form is: C = XY + XZ + YZ S = X'Y'Z + X'YZ'+XY'Z'+XYZ YZ X YZ X SumCarry S =  m(1,2,4,7) C =  m(3,5,6,7) Z

 Using K-map, simplified SOP form is: C = XY + XZ + YZ S = X'Y'Z + X'YZ'+XY'Z'+XYZ  We develop alternative formulae in terms of  using algebraic manipulation: C = XY + XZ + Y = XY + (X + Y)Z distr. law = XY + [ (X + Y)(1)]Z = XY + [(X + Y)((XY)’+(XY))] Z Thm.5 = XY + [(X + Y)(XY)’+ (X + Y)(XY)] Z distr. = XY + [(X + Y)(XY)’+ XXY+XYY] Z distr. = XY + [(X + Y)(XY)’+ XY] Z Thm.3, 3D = XY + [(X  Y) + XY] Z defn. of  = XY + (X  Y)Z + XYZ distr. = XY + (X  Y)Z Thm.10 S = X'Y'Z + X'YZ' + XY'Z' + XYZ = X'(Y'Z + YZ') + X(Y'Z' + YZ) distr. = X'(Y  Z) + X(Y  Z)‘ defn. of  = X  (Y  Z) defn. of  = X  Y  Z assoc. law for  Gate-level Design: Full Adder

 Circuit for above formulae: C = XY + (X  Y)Z S = X  Y  Z XYXY S C Z (XY) (X  Y) Full Adder made from two Half-Adders (+ OR gate). Gate-level Design: Full Adder

Full Adder made from two Half-Adders (+ OR gate). (X  Y) XYXY S C Z (XY) Half Adder Half Adder XYXY XYXY Sum Carry Sum Carry Block diagrams.  Circuit for above formulae: C = XY + (X  Y)Z S = X  Y  Z S C Z X Y H.A.