addition and subtraction
play

Addition and Subtraction Philipp Koehn 4 September 2019 Philipp - PowerPoint PPT Presentation

Aug 04, 2023 •151 likes •512 views

Addition and Subtraction Philipp Koehn 4 September 2019 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019 1 addition Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September

  1. Addition and Subtraction Philipp Koehn 4 September 2019 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  2. 1 addition Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  3. 1-Bit Adder 2 • Let’s start simple: Adding two 1-Bit numbers • Truth table A B A+B 0 0 0 0 1 1 1 0 1 1 1 10 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  4. Really 2 Operations 3 • Truth table for "position 0" bit A B A+B 0 0 0 xor 0 1 1 1 0 1 1 1 0 • Truth table for carry bit A B A+B carry 0 0 0 0 1 0 and 1 0 0 1 1 1 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  5. Reminder: Basic Gates 4 AND OR NOT NAND NOR Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  6. Circuits 5 • "Position 0" bit A B OUT0 A OR 0 0 0 B xor OUT0 0 1 1 AND 1 0 1 NAND 1 1 0 • Carry bit A B OUTC 0 0 0 A and OUTC AND 0 1 0 B 1 0 0 1 1 1 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  7. Putting them Together 6 A OR B OUT0 AND NAND CARRY AND Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  8. N-Bit Addition 7 011 +11 --- 110 --- 110 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  9. N-Bit Addition 8 011 +11 --- 110 --- 110 1+1 = 0, carry the 1 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  10. N-Bit Addition 9 011 +11 --- 110 --- 110 1+1+1 = 1, carry the 1 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  11. N-Bit Addition 10 011 +11 --- 110 --- 110 copy carry bit Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  12. 1-Bit Adder 11 A OR B OUT0 AND NAND CARRY AND Our adder cannot handle carry as input yet Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  13. Half 1-Bit Adder 12 A OR B OUT0 AND NAND CARRY AND 1-BIT HALF ADDER Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  14. Building a 1-Bit Full Adder 13 SUM A S A 1-BIT HALF B CARRY ADDER B C Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  15. Building a 1-Bit Full Adder 14 CARRY SUM S A 1-BIT HALF A CARRY ADDER S B A C 1-BIT HALF B CARRY ADDER B C Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  16. Building a 1-Bit Full Adder 15 SUM CARRY S A 1-BIT HALF A ADDER S B A C 1-BIT CARRY HALF OR B ADDER B C Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  17. 1-Bit Full Adder 16 SUM CARRY S A 1-BIT HALF A ADDER S B A C 1-BIT CARRY HALF OR B ADDER B C 1-BIT FULL ADDER Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  18. N-Bit Full Adder 17 011 +11 --- 110 --- 110 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  19. N-Bit Full Adder 18 B0 A0 011 +11 --- A B CI 110 1-BIT --- FULL 110 ADDER CO S SUM0 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  20. N-Bit Full Adder 19 B1 B0 A1 A0 011 +11 --- A B CI A B CI 110 1-BIT 1-BIT --- FULL FULL 110 ADDER ADDER CO S CO S SUM1 SUM0 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  21. N-Bit Full Adder 20 B2 B1 B0 A2 A1 A0 and so A B A B A B CI CI CI on 1-BIT 1-BIT 1-BIT ... FULL FULL FULL ADDER ADDER ADDER CO S CO S CO S SUM2 SUM1 SUM0 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  22. 21 subtraction Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  23. First, a Trick 22 • Normally, we subtract like this: 0253 -176 ---- 0110 ---- 0077 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  24. Computing the Inverse 23 • Now we use the inverse of the subtrahend 0999 -176 ---- 0823 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  25. Subtraction by Addition 24 • This allows us to carry our subtraction by addition 00253 +0823 ----- 01076 • Well, with minor corrections 01076 +0001 -1000 ----- 0077 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  26. Also Works in Binary 25 Original problem 00253 0011111101 -0176 -010110000 ----- ---------- 00077 0001001101 Inverse of subtrahend 00823 0001001111 Addition 00253 0011111101 +0823 +001001111 ----- ---------- 01076 0101001100 Corrections +0001 +000000001 -1000 -100000000 ---------- ---------- 0077 0001001101 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  27. Start with N-Bit Adder 26 A0 A1 A2 A3 B0 B1 B2 B3 4-BIT CI CO FULL ADDER S0 S1 S2 S3 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  28. Invert Bits of Subtrahend 27 B0 B1 B2 B3 A0 A1 A2 A3 B0 B1 B2 B3 4-BIT CI CO FULL ADDER S0 S1 S2 S3 Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  29. Add One 28 A0 A1 A2 A3 B0 B1 B2 B3 A0 A1 A2 A3 B0 B1 B2 B3 4-BIT V CI CO FULL ADDER S0 S1 S2 S3 Trick: add one as carry in Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  30. Invert Overflow --- DONE 29 A0 A1 A2 A3 B0 B1 B2 B3 A0 A1 A2 A3 B0 B1 B2 B3 4-BIT V CI CO FULL ADDER S0 S1 S2 S3 OVERFLOW SUM mm... Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  31. 30 unifying addition and subtraction machines Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  32. Goal 31 • Not two machines for addition and subtraction ⇒ Combined adder and subtractor • Input: A, B, and subtraction flag SUB • Output – if SUB=0: A+B – if SUB=1: A-B Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  33. NOT only if SUB 32 B0 B1 B2 B3 A0 A1 A2 A3 A0 A1 A2 A3 B0 B1 B2 B3 4-BIT V CI CO FULL ADDER S0 S1 S2 S3 OVERFLOW SUM mm... Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  34. NOT only if SUB 33 • Truth table SUB X OUT 0 0 0 0 1 1 1 0 1 1 1 0 • Looks like XOR XOR Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

  35. Combined Machine 34 A0 A1 A2 A3 B0 B1 B2 B3 SUB A0 A1 A2 A3 B0 B1 B2 B3 4-BIT SUB CI CO FULL ADDER SUB S0 S1 S2 S3 OVERFLOW SUM Philipp Koehn Computer Systems Fundamentals: Addition and Subtraction 4 September 2019

Recommend

2-Digit Subtraction Without Regrouping Click to return to Subtraction Table of Contents Slide 7

2-Digit Subtraction Without Regrouping Click to return to Subtraction Table of Contents Slide 7

Slide 1 / 137 Slide 2 / 137 2nd Grade 2 Digit Addition and Subtraction 2015-12-03 www.njctl.org Slide 3 / 137 Table of Contents Presentation 2 click on a topic to go to that section Mentally adding and subtracting 10 and 100 Addition

818 views • 46 slides
addition? Does less than always mean subtraction? Workshop Objectives To look at the

addition? Does less than always mean subtraction? Workshop Objectives To look at the

Questions Does more than always mean addition? Does less than always mean subtraction? Workshop Objectives To look at the different types of mathematical statements using more than and less than. To use Model Diagrams to

455 views • 24 slides
Arithmetic Operations Arithmetic Operations addition subtraction multiplication

Arithmetic Operations Arithmetic Operations addition subtraction multiplication

Arithmetic Operations Arithmetic Operations addition subtraction multiplication division Each of these operations on the integer representations: unsigned two's complement 1 Addition One bit of binary addition

681 views • 35 slides
Overflow in addition and subtraction can happen if?? ta7 What can

Overflow in addition and subtraction can happen if?? ta7 What can

Overflows Overflow in addition and subtraction can happen if?? ta7 What can we do if there is an overflow?? Spring 2006 MIPS support two kinds of arithmetic operations in order to support the two choices

50 views • 4 slides
Mental Maths Strategies Workshop 1: Addition and Subtraction 2014 1 Overview Workshop 1

Mental Maths Strategies Workshop 1: Addition and Subtraction 2014 1 Overview Workshop 1

Mental Maths Strategies Workshop 1: Addition and Subtraction 2014 1 Overview Workshop 1 Workshop 2 May 2014 School year 2014/2015 Addition and Multiplication and subtraction division strategies strategies 2 Support

397 views • 29 slides
Systems Addition and Subtraction in 1s and 2s Complement Form Shankar Balachandran*

Systems Addition and Subtraction in 1s and 2s Complement Form Shankar Balachandran*

Spring 2015 Week 9 Module 49 Digital Circuits and Systems Addition and Subtraction in 1s and 2s Complement Form Shankar Balachandran* Associate Professor, CSE Department Indian Institute of Technology Madras *Currently a Visiting

341 views • 13 slides
Addition and Subtraction at Leighterton Overview of the session 9.00 a.m. 9.30 a.m.

Addition and Subtraction at Leighterton Overview of the session 9.00 a.m. 9.30 a.m.

Addition and Subtraction at Leighterton Overview of the session 9.00 a.m. 9.30 a.m. Presentation (hall) 9.30 a.m. 10.00 a.m. Workshops (classrooms) 10.00 a.m. 10.15 a.m. Celebration assembly (hall) Aims for the session

1.26k views • 26 slides
Focus on Fractions - Addition and Subtraction with Unlike Denominators with Lisa Riggs Welcome!

Focus on Fractions - Addition and Subtraction with Unlike Denominators with Lisa Riggs Welcome!

Focus on Fractions - Addition and Subtraction with Unlike Denominators with Lisa Riggs Welcome! Your host Lisa Riggs Regional Consultant Kentucky Center for Mathematics lriggs2@murraystate.edu KCM Website www.kentuckymathematics.org

622 views • 25 slides
Fraction Focus: Addition & Subtraction with Common Denominators Your host Leah Dix White

Fraction Focus: Addition & Subtraction with Common Denominators Your host Leah Dix White

Fraction Focus: Addition & Subtraction with Common Denominators Your host Leah Dix White Regional Consultant Kentucky Center for Mathematics leah.dix@louisville.edu Visit Our Website www.kentuckymathematics.org Todays Session

419 views • 26 slides
Subtraction games with expandable subtraction sets Bao Ho Department of Mathematics and

Subtraction games with expandable subtraction sets Bao Ho Department of Mathematics and

The game of Nim Sprague-Grundy function Subtraction games Periodicity of subtraction games Expansion of subtraction sets Subtraction games with expandable subtraction sets Bao Ho Department of Mathematics and Statistics La Trobe University

452 views • 34 slides
C Programming for Engineers Arrays & Pointers ICEN 360 Spring 2017 Prof. Dola Saha 1

C Programming for Engineers Arrays & Pointers ICEN 360 Spring 2017 Prof. Dola Saha 1

C Programming for Engineers Arrays & Pointers ICEN 360 Spring 2017 Prof. Dola Saha 1 Classroom Assignment Matrix Addition/Subtraction two matrices should have same number of rows and columns. Addition Subtraction

478 views • 30 slides
Lecture 8: Binary Multiplication & Division Todays topics: Addition/Subtraction

Lecture 8: Binary Multiplication & Division Todays topics: Addition/Subtraction

Lecture 8: Binary Multiplication & Division Todays topics: Addition/Subtraction Multiplication Division Reminder: get started early on assignment 3 1 2s Complement Signed Numbers 0000 0000 0000 0000 0000 0000

873 views • 20 slides
Modular Arithmetic Addition and Subtraction Modulus 9 0 mod 9 = 0 9 mod 9 = 0 1 mod 9 = 1 10

Modular Arithmetic Addition and Subtraction Modulus 9 0 mod 9 = 0 9 mod 9 = 0 1 mod 9 = 1 10

Modular Arithmetic Addition and Subtraction Modulus 9 0 mod 9 = 0 9 mod 9 = 0 1 mod 9 = 1 10 mod 9 = 1 0 2 mod 9 = 2 11 mod 9 = 2 8 1 3 mod 9 = 3 12 mod 9 = 3 7 2 4 mod 9 = 4 13 mod 9 = 4 5 mod 9 = 5 14 mod 9 = 5 6 3 6 mod 9 =

212 views • 8 slides
Review 1 Single Digit Addition: 5 + 2 = ? Two Digit Addition: Review 1 Continued Doubling: 7 + 7

Review 1 Single Digit Addition: 5 + 2 = ? Two Digit Addition: Review 1 Continued Doubling: 7 + 7

Hi Everyone Welcome to class! July 28 Review 1 Single Digit Addition: 5 + 2 = ? Two Digit Addition: Review 1 Continued Doubling: 7 + 7 = ? Halving: Opposite Operations Double and half are opposite operations Addition and subtraction

768 views • 42 slides
Mathematics 2 2-1a Vectors and Matrices Vector Addition and Subtraction Example (FEIM): What is

Mathematics 2 2-1a Vectors and Matrices Vector Addition and Subtraction Example (FEIM): What is

Mathematics 2 2-1a Vectors and Matrices Vector Addition and Subtraction Example (FEIM): What is the resultant of vectors F 1 , F 2 , and F 3 ? F 1 = 5 i + 6 j + 3 k F 2 = 11 i + 2 j + 9 k F 3 = 7 i 6 j 4 k R = (5 + 11 + 7) i + (6 + 2

437 views • 42 slides
Addition Identity For Sine MHF4U: Advanced Functions Consider the following triangle. Addition

Addition Identity For Sine MHF4U: Advanced Functions Consider the following triangle. Addition

t r i g o n o m e t r i c i d e n t i t i e s t r i g o n o m e t r i c i d e n t i t i e s Addition Identity For Sine MHF4U: Advanced Functions Consider the following triangle. Addition and Subtraction Identities J. Garvin Since | AC | = 1, |

429 views • 3 slides
Lets Do Math with KCM- Middle Grades Addition & Subtraction of Fractions & Decimals

Lets Do Math with KCM- Middle Grades Addition & Subtraction of Fractions & Decimals

Lets Do Math with KCM- Middle Grades Addition & Subtraction of Fractions & Decimals Welcome! Your host Cindy Aossey Regional Consultant Kentucky Center for Mathematics cindy.aossey@outlook.com Kentucky Center for Mathematics

455 views • 29 slides
Com Compatible patible Pairs Pair Compatible Pairs for addition and subtraction are numbers

Com Compatible patible Pairs Pair Compatible Pairs for addition and subtraction are numbers

75 and 25 make 100 6 and 4 make 10 Com Compatible patible Pairs Pair Compatible Pairs for addition and subtraction are numbers which go together to make nice numbers. The tasks in this booklet get students accustomed to looking for

371 views • 9 slides
Class 8: Relative velocity and projectile motion Vector operations without a coordinate system

Class 8: Relative velocity and projectile motion Vector operations without a coordinate system

Class 8: Relative velocity and projectile motion Vector operations without a coordinate system Addition and subtraction of vectors Addition: Subtraction: A B A B B Sine and cosine rules A c b B C a Cosine rules: 2 2 2 a

337 views • 7 slides
Subtraction Strategies Grades 3-5: Providing Hope Lori Williams, Ph.D.

Subtraction Strategies Grades 3-5: Providing Hope Lori Williams, Ph.D.

Addition & Subtraction Strategies Grades 3-5: Providing Hope Lori Williams, Ph.D. dr.loriwilliams@sbcglobal.net 121 Facts to Go + 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 1. Zero Property + 0 1 2 3

745 views • 13 slides
Decimal Addition Return to Table of Contents Slide 5 / 152 Place Value Chart Slide 6 / 152

Decimal Addition Return to Table of Contents Slide 5 / 152 Place Value Chart Slide 6 / 152

Slide 1 / 152 Slide 2 / 152 5th Grade Decimal Computation 2015-10-08 www.njctl.org Slide 3 / 152 Decimal Computation Unit Topics Click on the topic to go to that section Decimal Addition Decimal Subtraction Multiplication of

971 views • 51 slides
Numb3rs 0 12 1 11 2 10 3 Z = { ..., -2, -1, 0, 1, 2, ... } 9 4 8 5 N = { 0, 1, 2, ... }

Numb3rs 0 12 1 11 2 10 3 Z = { ..., -2, -1, 0, 1, 2, ... } 9 4 8 5 N = { 0, 1, 2, ... }

Numb3rs 0 12 1 11 2 10 3 Z = { ..., -2, -1, 0, 1, 2, ... } 9 4 8 5 N = { 0, 1, 2, ... } 7 6 Z + = { 1, 2, ... } Quotient & Remainder & addition, subtraction and multiplication Divisibility Definition: For n,d Z , d|n (d

316 views • 6 slides
Connecting enactive/iconic/symbolic models to mathematical problem types for addition and

Connecting enactive/iconic/symbolic models to mathematical problem types for addition and

Connecting enactive/iconic/symbolic models to mathematical problem types for addition and subtraction February 3, 2017 Emilie Eisenberger & Kelli Rich Whittier Elementary, Boise School District Dr. Jonathan Brendefurs research has

368 views • 35 slides
Software and Foreground Subtraction Dave McGinnis 4/26/2010 Foreground Subtraction - McGinnis

Software and Foreground Subtraction Dave McGinnis 4/26/2010 Foreground Subtraction - McGinnis

21cm Instrument Simulation Software and Foreground Subtraction Dave McGinnis 4/26/2010 Foreground Subtraction - McGinnis 1 SKY SIMULATION SOFTWARE 4/26/2010 Foreground Subtraction - McGinnis 2 Code Suite 20 Java classes organized into

727 views • 34 slides

More recommend