1 Engineering Mathematics 1 (AQB10102) CHAPTER 1: NUMBERS AND ARITHMETIC 1.1 TYPE OF NUMBERS NEGATIVE INTEGER - POSITIVE AND REAL NUMBERS (R) • • Numbers that can be expressed as decimals Real Number System: • Consist of positive and negative natural numbers including 0 Example: …‚ -5‚ -4‚ -3‚ -2‚ -1‚ 0‚ 1‚ 2‚ 3‚ 4‚ 5‚ … • All numbers including natural numbers‚ whole numbers‚ integers‚ rational numbers and irrational numbers are real numbers Example: 4 = 4
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Why the knowledge of the binary numbering system is essential * The binary numbering system plays a central role in how information of all kinds is stored on the computer. Understanding binary can lift a lot of the mysteries from computers because at a fundamental level they’re really just machines for flipping binary digits on and off. There are several activities on binary numbers in this document‚ all simple enough that they can be used to teach the binary system to anyone who can count
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CPEN 214 - Digital Logic Design Binary Systems C. Gerousis © Digital Design 3rd Ed.‚ Mano Prentice Hall Digital vs. Analog • An analog system has continuous range of values – A mercury thermometer – Vinyl records – Human eye • A digital system has a set of discrete values – Digital Thermometer – Compact Disc (CD) – Digital camera Benefits of using digital Analog signal Digital signal • Advantages of using Digital: • Cheap electronic circuits • Easier to calibrate and adjust • Resistance
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numbers. Let’s consider an example on math: 191‚350‚000‚000‚000 = 1.9135 x 1014 -0.000 000 000 019 135 = -1.9135 x 10-11 Thus all the number can be expressed with a base value and a scaling factor. The scaling factor plays role in moving the decimal point so that the name of “floating point” number is originated from this. With the float number in C++‚ the computer stores a value in three parts: one represents the precision of value‚ the other part scales that shows the range of value and other
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Activity 2.3.1 Hexadecimal and Octal Number Systems Introduction We all know that digital electronics use the binary number system. However‚ with new computers containing 32‚ 64‚ and even 128 bit data busses‚ displaying numbers in binary is quite cumbersome. For example‚ a single piece of data on a 64-bit data bus would look like this: 0110100101110001001101001100101001101001011100010011010011001010 Obviously‚ presenting data in this form would invite error. For this reason we use the hexadecimal
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use computer math with computer hardware and systems. Some of these concepts are bits versus bytes‚ binary versus decimal‚ Boolean operators‚ hertz‚ and data transfer. The chapter two also shows numbering systems used in computers. These are some importance skills that will help you in the computer field. Thirty plus years ago‚ the first personal computer terms such as bits‚ bytes‚ decimal‚ binary‚ and hexadecimal have come part of the common language‚ but these terms are not always used correctly
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arithmetic operations :Using binary signed 2’s complement notation for integers. You may assume that the maximum size of integers is of 9 bits including the sign bit. (Please note that the numbers given here are in decimal notation). i) Add – 256 and 206 ii) Subtract 224 from –99 iii) Add 124 and 132 Please indicate the overflow if it occurs. Also write how you identify overflow. i) Add – 256 and 206 First‚ we have to represent the number in binary notation The sign of a binary number is represented by
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Reading Binary Exercise 1.1.1 Create a mapping similar to Figure 1- 1 for the decimal number 2931 using either paper and pencil or a Word document. Exercise 1.1.2 Create a mapping similar to Figure 1- 2 for the binary number 110 2 using either paper and pencil or a Word document. Exercise 1.1.3 Create a mapping similar to Figure 1- 2 for the binary number 11 2 using either paper and pencil or a Word document. Exercise 1.1.4 Create an expanded mapping similar to Figure 1- 3 for the binary number
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Answer 3. What would you call a device that works with binary data? Any device that works with binary data is called a digital device. 5. What are the short words that are used in assembly language called? Assembly language uses short words known as mnemonics for instructions in a program. Exercises 1. Use what you’ve learned about the binary numbering system in this chapter to convert the following decimal numbers to binary: 11 00001011 65 01000001 100 01100100
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8:30-12:30 6/25/2013 Exercise 1.1 Base 10 Mapping for decimal number 2931 10^3 10^2 10^1 10^0 2 9 3 1 2x1000=2000 + 9x100=900 + 3x10=30 + 1x1=1 = 2931 Exercise 1.1.2 Mapping for binary number 110 base 2 4 2 1 * * * 1 1 0 = = = 4 + 2 + 0= 6 Exercise 1.1.3 Mapping for binary number 11 base 2 2 1 * * 1 1 = = 2 + 1= 3 Exercise 1.1.4 Mapping for binary number 10010 base 2 16 8 4 2 1 * * * * * 1 0 0 1 0 = = = =
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