Figure5.2 Half-adder x i y i c 00 01 11 10 i 1 1 0 c i x - PDF document

Oct 31, 2023 •153 likes •232 views

x 0 0 1 1 + y + 0 + 1 + 0 + 1 c s 0 0 0 1 0 1 1 0 Carry Sum (a) The four possible cases Carry Sum x y c s 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 (b) Truth table x s y x s HA y c c (c) Circuit (d)

x 0 0 1 1 + y + 0 + 1 + 0 + 1 c s 0 0 0 1 0 1 1 0 Carry Sum (a) The four possible cases Carry Sum x y c s 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 (b) Truth table x s y x s HA y c c (c) Circuit (d) Graphical symbol Figure5.2 Half-adder
x i y i c 00 01 11 10 i 1 1 0 c i x i y c s i i + 1 i 1 1 1 0 0 0 0 0 0 0 1 0 1 s = x y c ⊕ ⊕ i i i i 0 1 0 0 1 0 1 1 1 0 x i y i 1 0 0 0 1 c 00 01 11 10 i 1 0 1 1 0 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 (a) Truth table c = x i y + x i c + y i c i + 1 i i i (b) Karnaugh maps x i y s i i c i c i + 1 (c) Circuit Figure5.4 Full-adder
A : a a 7 0 x x y y 7 0 7 0 c 7 s s 7 0 0 x x x y y y 8 7 0 8 7 0 c 8 s s 8 0 = 3 : P A P P P 9 8 0 (a) Naive approach A : a a 7 0 0 0 x x 1 x y y y 8 0 8 7 0 c 8 s s 8 0 : P = 3 A P P P 9 8 0 (b) Efficient design Figure5.7 Circuit that multiplies an 8-bit unsigned number by 3
Multiplicand M (14) 1 1 1 0 Multiplier Q (11) 1 0 1 1 × 1 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 Product P (154) 1 0 0 1 1 0 1 0 (a) Multiplication by hand Multiplicand M (11) 1 1 1 0 Multiplier Q (14) × 1 0 1 1 Partial product 0 1 1 1 0 + 1 1 1 0 Partial product 1 1 0 1 0 1 + 0 0 0 0 Partial product 2 0 1 0 1 0 + 1 1 1 0 Product P (154) 1 0 0 1 1 0 1 0 (b) Multiplication for implementation in hardware Figure5.32 Multiplication of unsigned numbers
0 m m m m 3 2 1 0 q 0 0 PP1 q 1 q 2 0 PP2 q 3 0 p p p p p p p p 7 6 5 4 3 2 1 0 (a) Structure of the circuit m m k + 1 k Bit of PPi m k q 0 q q j 1 c c c c FA FA out out in in (b) A block in the top row (c) A block in the bottom two rows Figure5.33 A 4 x 4 multiplier circuit
Multiplicand M (+14) 0 1 1 1 0 x Multiplier Q (+11) 0 1 0 1 1 Partial product 0 0 0 0 1 1 1 0 + 0 0 1 1 1 0 Partial product 1 0 0 1 0 1 0 1 + 0 0 0 0 0 0 Partial product 2 0 0 0 1 0 1 0 + 0 0 1 1 1 0 Partial product 3 0 0 1 0 0 1 1 + 0 0 0 0 0 0 Product P (+154) 0 0 1 0 0 1 1 0 1 0 (a) Positive multiplicand Multiplicand M ( 14) – 1 0 0 1 0 Multiplier Q (+11) 0 1 0 1 1 × Partial product 0 1 1 1 0 0 1 0 + 1 1 0 0 1 0 Partial product 1 1 1 0 1 0 1 1 0 0 0 0 0 0 + Partial product 2 1 1 1 0 1 0 1 + 1 1 0 0 1 0 Partial product 3 1 1 0 1 1 0 0 + 0 0 0 0 0 0 – Product P ( 154) 1 1 0 1 1 0 0 1 1 0 (b) Negative multiplicand Figure5.34 Multiplication of signed numbers
Table 5.4 The seven-bit ASCII code

Recommend

ex start small with a 1-bit (half) adder A B Carry out Sum A 0 0 Sum 0 1 B 1 0 1 1

Addition: ex start small with a 1-bit (half) adder A B Carry out Sum A 0 0 Sum 0 1 B 1 0 1 1 Carry out Carry in ex 1-bit full adder A + Sum B Carry out n-bit addition: Sum i = A i + B i + CarryOut i-1 Need a bigger adder!

328 views • 12 slides

Combinatorial networks- II Digital Systems M 1 Adder Lets see the truth table of a

Combinatorial networks- II Digital Systems M 1 Adder Lets see the truth table of a combinatorial network whose output values correspond to the numerical values of a 2-bit adder (Half Adder) ab Sum Carry 00 0

852 views • 64 slides

Outline Introduction to CMOS VLSI Single-bit Addition Design Carry-Ripple Adder

Outline Introduction to CMOS VLSI Single-bit Addition Design Carry-Ripple Adder Carry-Skip Adder Carry-Lookahead Adder Lecture 11: Carry-Select Adder Adders Carry-Increment Adder Tree Adder David Harris Harvey Mudd

193 views • 8 slides

Lesson 7 Combinational Logic Circuits Concepts Introduced Adders Multiplexers

Lesson 7 Combinational Logic Circuits Concepts Introduced Adders Multiplexers Decoders basic Arithmetic/Logic Unit Review Half-Adder A half adder takes two inputs, a and b, and generates two outputs, the carry and the sum.

354 views • 32 slides

FAST TWO-OPERAND ADDITION A. Conventional number system. Carry-propagate adders (CPA)

1 FAST TWO-OPERAND ADDITION A. Conventional number system. Carry-propagate adders (CPA) Switched carry-ripple adder Carry-skip adder Carry-lookahead adder Prefix adder Carry-select adder and conditional-sum adder

921 views • 57 slides

ex Addition: 1-bit half adder A + Sum B Carry out Carry A B Sum out 0 0 A 0 1 Sum

ex Addition: 1-bit half adder A + Sum B Carry out Carry A B Sum out 0 0 A 0 1 Sum B 1 0 1 1 Carry out Carry in ex Addition: 1-bit full adder A + Sum B Carry out Carry Carry Carry in A B Sum in out 0 0 0 A 0

343 views • 12 slides

Problem 1 Design a Verilog 16-bit adder module module adder (A, B, sum); input [15:0] A, B;

Problem 1 Design a Verilog 16-bit adder module module adder (A, B, sum); input [15:0] A, B; output [15:0] sum; assign sum = A + B; endmodule Problem 1 Design a Verilog 16-bit adder module module adder (A, B, sum); input [15:0] A,

653 views • 22 slides

CSE 140 Lecture 13 Standard Combinational Modules CK Cheng CSE Dept. UC San Diego Some slides

CSE 140 Lecture 13 Standard Combinational Modules CK Cheng CSE Dept. UC San Diego Some slides from Harris and Harris 1 Part III. Standard Modules Interconnect Operators. Representation of numbers Adders 1. Full Adder 2. Half Adder 3.

689 views • 45 slides

Continuations Control flow of Web applications Michel Schinz 20070504 The adder

Continuations Control flow of Web applications Michel Schinz 20070504 The adder application The adder Web application Lets assume that we want to take our adder application and turn it into a Web application, with the requirement

463 views • 7 slides

I'm Etienne React trainer & dev & consultant @LeReacteurIO A Binary adder written

Hi I'm Etienne React trainer & dev & consultant @LeReacteurIO A Binary adder written with TypeScript types only Binary what ? An adder is a digital circuit that performs addition of numbers. Yes, we are just trying to

444 views • 32 slides

Learning Outcomes I understand what gates are used to design half and full adders Unit 12

12.1 12.2 Learning Outcomes I understand what gates are used to design half and full adders Unit 12 I can build larger arithmetic circuits from smaller building blocks Adders & Arithmetic Circuits 12.3 12.4 Adder Intro

278 views • 10 slides

5. Simulate the n-bit modular adder/subtracter architecture The modular adder/subtracter performs

Summer School on Real-world Crypto and Privacy Hardware tutorial June 14, 2018, ibenik, Croatia Nele Mentens (KU Leuven) Pedro Maat Costa Massolino (Radboud University) TUTORIAL INSTRUCTIONS In this tutorial, we will design and simulate a

74 views • 4 slides

TV VA Brightness Adder 09/04/19 EPA Luminance Requirements For products with a luminance in

TV VA Brightness Adder 09/04/19 EPA Luminance Requirements For products with a luminance in the Brightest Selectable Preset Picture Setting (the greater value of L DEFAULT_RETAIL or L BRIGHTEST_HOME) less than 350 cd/m2, luminance in the

412 views • 6 slides

Regulating attention We hear half of what is said (50%) We listen to half of that

Listening well-while attending a Yannis Theodorakis lecture Regulating attention We hear half of what is said (50%) We listen to half of that (25%) and concentration We understand half of them (12.5%) We believe half

457 views • 13 slides

Behavioral Modeling Using continuous assignments ISE can build you a nice adder Easier

Verilog Synthesis Examples CS/EE 3710 Fall 2010 Mostly from CMOS VLSI Design by Weste and Harris Behavioral Modeling Using continuous assignments ISE can build you a nice adder Easier than specifying your own 1 Bitwise Operators

471 views • 19 slides

Continuations Michel Schinz 20070504 Control flow of Web applications The adder

Continuations Michel Schinz 20070504 Control flow of Web applications The adder application The following Scheme program asks for two numbers, and displays their sum assuming the obvious definitions for prompt-int and display-int :

748 views • 42 slides

Verifying Centaurs Floating Point Adder Sol Swords sswords@cs.utexas.edu April 23, 2008 Sol

Verifying Centaurs Floating Point Adder Sol Swords sswords@cs.utexas.edu April 23, 2008 Sol Swords () Verifying Centaurs Floating Point Adder April 23, 2008 1 / 21 Problem Given: Verilog RTL for the Centaur CN processors FADD

898 views • 21 slides

Efficient Structural Adder Pipelining in Transposed Form FIR Filters International Conference on

Efficient Structural Adder Pipelining in Transposed Form FIR Filters International Conference on Digital Signal Processing 23 July 2015 Mathias Faust , Martin Kumm * , Chip-Hong Chang and Peter Zipf * Nanyang Technological

476 views • 33 slides

A Number System Approach for Adder Topologies lvaro Vzquez REPSOL-ITMATI Technological

A Number System Approach for Adder Topologies lvaro Vzquez REPSOL-ITMATI Technological Institute For Industrial Mathematics Elisardo Antelo University of Santiago de Compostela Spain Introduction Mathematical Foundation behind the

555 views • 19 slides

Systems Fast Adder Shankar Balachandran* Associate Professor, CSE Department Indian Institute

Spring 2015 Week 9 Module 51 Digital Circuits and Systems Fast Adder Shankar Balachandran* Associate Professor, CSE Department Indian Institute of Technology Madras *Currently a Visiting Professor at IIT Bombay Recursive Doubling Technique

475 views • 24 slides

Lecture 13: Sequential Circuits Todays topics: Carry-lookahead adder Clocks and

Lecture 13: Sequential Circuits Todays topics: Carry-lookahead adder Clocks and sequential circuits Finite state machines Reminder: Assignment 5 due on Thursday 10/12, mid-term exam Tuesday 10/24 1 Speed of

281 views • 25 slides

CSCI-2500 Computer Organization Carry-Lookahead (CLA) Adder Justin M. LaPre Department of

CSCI-2500 Computer Organization Carry-Lookahead (CLA) Adder Justin M. LaPre Department of Computer Science Rensselaer Polytechnic Institute 110 8th Street Troy, New York U.S.A. 12180 March 14, 2016 1 Equation Dependencies for 64 Bit CLA

230 views • 3 slides

Systems Ripple Carry Adder Shankar Balachandran* Associate Professor, CSE Department Indian

Spring 2015 Week 9 Module 50 Digital Circuits and Systems Ripple Carry Adder Shankar Balachandran* Associate Professor, CSE Department Indian Institute of Technology Madras *Currently a Visiting Professor at IIT Bombay Adders and

911 views • 11 slides

EE 457 Unit 2b Fast Adders (Carry-Lookahead Adder) 2 Carry-Lookahead Adders FAST ADDERS 3

1 EE 457 Unit 2b Fast Adders (Carry-Lookahead Adder) 2 Carry-Lookahead Adders FAST ADDERS 3 Ripple Carry Adder Critical Path Critical Path = Longest possible delay path Assume t sum = 5 ns, t carry = 4 ns X Y X Y X Y X Y 16 ns

467 views • 18 slides