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GCSE Computing Theory © gcsecomputing.net 1 GCSE Computing 2.14 Data Representation Binary Arithmetic
Learning Objectives: 2 add two 8-bit binary integers explain overflow errors which may occur GCSE Computing GCSE Computing Theory © gcsecomputing.net
Decimal Arithmetic Rules 3 ADDdenarydenary sum = 7= = 15= 5 (carry 1) GCSE Computing GCSE Computing Theory © gcsecomputing.net
Adding Decimal Numbers Carry + GCSE Computing GCSE Computing Theory © gcsecomputing.net
Adding Decimal Numbers Carry + 1 GCSE Computing GCSE Computing Theory © gcsecomputing.net
Binary Arithmetic Rules 6 ADDdenarybinarybinary sum = 0= 00= = 1= 01= = 1= 01= = 2= 10= 0 (carry 1) = 3= 11= 1 (carry 1) GCSE Computing GCSE Computing Theory © gcsecomputing.net
Adding Binary Numbers Carry Decimal AdditionBinary Addition 1 GCSE Computing GCSE Computing Theory © gcsecomputing.net
Adding Binary Numbers Carry Decimal AdditionBinary Addition 1 GCSE Computing 1 1 GCSE Computing Theory © gcsecomputing.net
Overflow in Binary Number Addition Carry Decimal AdditionBinary Addition GCSE Computing If we only have 4 bits to store the result there would be no room for a carry, so it is lost and we get the wrong answer. When there isn’t enough room for a result, this is called an overflow and it produces an overflow error. GCSE Computing Theory © gcsecomputing.net
1 A Simple ALU Binary Logic. 2 Outline l Binary Logic l Representation of Logic Gates l Constructing a 1-bit adder l Constructing an n-bit adder.
GCSE Computing Theory © gcsecomputing.net 1 GCSE Computing Data Representation Why Binary?
Representing Numbers B261 Systems Architecture. Previously Computer Architecture –Common misconceptions –Performance Instruction Set (MIPS) –How data.
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1 Binary Numbers. 2 Main Memory Main memory holds information such as computer programs, numeric data, or documents created by a word processor. Main.
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CHAPTER 2 Introduction to Integers and Algebraic Expressions Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2.1Integers and the Number.
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©2008 The McGraw-Hill Companies, Inc. All rights reserved. Digital Electronics Principles & Applications Seventh Edition Chapter 2 Numbers We Use in Digital.
Digital Logic & Design Lecture No. 3. Number System Conversion Conversion between binary and octal can be carried out by inspection. Each octal digit.
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BY GRAPHING Y = 2X + 1 Y = -X + 4 (1,3) IS THE SOLUTION.
Chapter 2 Binary Values and Number Systems Chapter Goals Distinguish among categories of numbers Describe positional notation Convert numbers in.
Arithmetic Calculations n Basic arithmetic operators: + addition - subtraction * multiplication / division %remainder (or modulus). Same precedence and.
Factoring Patterns There is a pattern for factoring trinomials of this form, when c is positive x² + bx + c.
6.1 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Chapter 2 Data Encryption Standard (DES)
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© 2007 Lawrenceville Press Slide 1 Assignment Statement An assignment statement gives a value to a variable. Assignment can take several forms: x = 5;
Objectives: Understand that algebraic operations follow the same rules as arithmetic operations. Solve simple equations Transform information from words.
Adders Used to perform addition, subtraction, multiplication, and division (sometimes) Half-adder adds rightmost (least significant) bit Full-adder.
Daily Quiz - Simplify the expression, then create your own realistic scenario for the final expression.
Modular Arithmetic Several important cryptosystems make use of modular arithmetic. This is when the answer to a calculation is always in the range 0 –
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1 Tandi Clausen-May Teaching Maths to Pupils with Different Learning Styles London: Paul Chapman, 2005 Click the mouse. Click the mouse only when you seeClick.
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15 October 2013Birkbeck College, U. London1 Introduction to Computer Systems Lecturer: Steve Maybank Department of Computer Science and Information Systems.
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