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EET 1131. Digital Electronics Professor Nick Reeder. Reminders. Please turn off cell phones. No food or soft drinks in the classroom. Stow water bottles at floor level. EET 1131 Unit 1 Number Systems and Codes. Read Kleitz , Chapter 1 (but skip Sections 1-6 and 1-7).

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## EET 1131

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**EET 1131**Digital Electronics Professor Nick Reeder**Reminders**• Please turn off cell phones. • No food or soft drinks in the classroom. • Stow water bottles at floor level.**EET 1131 Unit 1 Number Systems and Codes**• Read Kleitz, Chapter 1 (but skip Sections 1-6 and 1-7). • Homework #1 and Lab #1 due next week. • Quiz next week.**Analog versus Digital**• Analog = continuous • Digital = discrete • Example: • An analog clock, whose hands move smoothly and continuously. • A digital clock, whose digits jump from one value to the next.**Analog Quantities**Most natural quantities (such as temperature, pressure, light intensity, …) are analogquantities that vary continuously. Digital systems can process, store, and transmit data more efficiently but can only assign discrete values to each point.**The Digital Revolution**• Recently, many types of devices have been converted from analog to digital. • Examples: • In all of these digital devices, info is stored and transmitted as long strings of 1s and 0s.**Analog and Digital Systems**Many systems use a mix of analog and digital electronics to take advantage of each technology. A typical CD player accepts digital data from the CD drive and converts it to an analog signal for amplification.**Voltage**• Voltage is a basic electrical quantity that is important in all circuits (analog or digital). • You can think of a circuit as being like a plumbing system, with water flowing through pipes. • On this analogy, voltage is like the water pressure in the pipes. Its value will vary at different points in the circuit.**A Simple Circuit**A wire is like a water pipe. The amount of electricity flowing through a wire is called current, which is measured in amperes. The voltage (pressure) at this point is greater than the voltage at this point. A voltage source is like a water pump. Its voltage rating (in volts) tells you how strong it is. Resistors are like partial blockages in the pipe. They restrict the amount of current that flows through the circuit.**Examples of Voltage Sources**• Voltage is measured in volts (V). • Flashlight battery ____ V • Wall outlet ____ V**Trainer Power Supplies**Fixed +5 V supply: In this course we’ll always use this one. No matter which one of these you use, you must also use the GROUND connection. Variable supplies, controlled by the knobs at left. You’ll use these in other courses.**Measuring Exact Voltage**• In other courses you’ll use a voltmeter or digital multimeter, like the one shown, to measure the exact voltage at a point in a circuit.**Measuring Digital HIGHS or LOWS**• In this course we usually don’t care about exact voltage values. We just care whether the voltage at a point is “high” or “low.” • To measure this, we use a logic probe, such as the one shown.**Binary Digits and Logic Levels**Digital electronics uses circuits that have two states, which are represented by two voltage ranges called HIGH and LOW. We often represent a HIGH state by the number 1, and a LOW state by the number 0. VH(max) HIGH VH(min) Invalid VL(max) LOW VL(min)**Breadboarding Guidelines**• When you build circuits in lab, I expect you to follow the breadboarding guidelines on the course website.**Ones and Zeros**• Digital devices (computers, iPods, cell phones, …) store information (numbers, text, images, music, …) as strings of 1s and 0s. • Each 1 or 0 in such a string is called a bit (short for binary digit). • Example of an 8-bit string: 01101100 • A typical song in an MP3 file might contain 40 million bits.**Number Systems and Codes**• This week we’ll look mainly at how to represent numbers using 1s and 0s, and also (briefly) how to represent text using 1s and 0s.**Binary Number System**• When we represent numbers using 1s and 0s, we’re using the binary number system. This system is fundamental to everything in digital electronics, so you must learn it thoroughly. • First, we’ll briefly review the decimal number system that you’ve used for most of your life.**Decimal Numbers**The position of each digit in a weighted number system is assigned a weight based on the base or radix of the system. The base of decimal numbers is ten, because only ten symbols (0 through 9) are used to represent any number. The column weights of decimal numbers are powers of ten that increase from right to left beginning with 100 =1: …105 104 103 102 101 100.**Decimal Numbers**Decimal numbers can be expressed as the sum of the products of each digit times the column value for that digit. Thus, the number 9240 can be expressed as (9 x 103) + (2 x 102) + (4 x 101) + (0 x 100) or 9 x 1,000 + 2 x 100 + 4 x 10 + 0 x 1 Example Express the number 480 as the sum of values of each digit. Solution 480 = (4 x 102) + (8 x 101) + (0 x 100)**Binary Numbers**For digital systems, the binary number system is used. Binary has a base of two and uses the digits 0 and 1 to represent quantities. The column weights of binary numbers are powers of two that increase from right to left beginning with 20 =1: …25 24 23 22 21 20.**Decimal Number**Binary Number Binary Numbers 0 0 0 0 0 1 0 0 0 1 2 0 0 1 0 3 0 0 1 1 4 0 1 0 0 5 0 1 0 1 6 0 1 1 0 7 0 1 1 1 8 1 0 0 0 9 1 0 0 1 10 1 0 1 0 11 1 0 1 1 12 1 1 0 0 13 1 1 0 1 14 1 1 1 0 15 1 1 1 1 A binary counting sequence for numbers from zero to fifteen is shown. Notice the pattern of zeros and ones in each column.**Binary-to-Decimal Conversions**The decimal equivalent of a binary number can be determined by adding the column values of all of the bits that are 1 and discarding all of the bits that are 0. Example Convert the binary number 100101 to decimal. Solution Start by writing the column weights; then add the weights that correspond to each 1 in the number. 32 16 8 4 2 1 1 0 0 1 0 1 32 +4 +1 = 37**Decimal-to-Binary Conversions (First Method)**You can convert a decimal whole number to binary by reversing the procedure. Write the decimal weight of each column and place 1’s in the columns that sum to the decimal number. Example Convert the decimal number 49 to binary. Solution The column weights double in each position to the right. Write down column weights until the last number is larger than the one you want to convert. 64 32 16 8 4 2 1. 0 1 1 0 0 0 1.**remainder**49 2 Decimal number base Quotient Decimal-to-Binary Conversions (Second Method) You can convert decimal to any other base by repeatedly dividing by the base. For binary, repeatedly divide by 2: Convert the decimal number 49 to binary by repeatedly dividing by 2. Example Solution You can do this by “reverse division” and the answer will read from left to right. Put quotients to the left and remainders on top. Answer: 1 1 0 0 0 1 0 1 3 6 12 24 Continue until the last quotient is 0**The Hexadecimal and Octal Systems**• We’ve looked at the decimal and binary systems. • Hexadecimal (often called “hex”) and octal are useful as shorthand systems of writing large binary numbers. • Hex is a base-16 system. • Octal is a base-8 system. • Hex is very widely used. • Octal was popular 40 years ago, but is not used much today.**Decimal**Hexadecimal Binary Hexadecimal Numbers 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1415 0 1 2 3 4 5 6 7 8 9 A B C D E F 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 Hexadecimal uses sixteen characters to represent numbers: the numbers 0 through 9 and the alphabetic characters A through F. Large binary numbers can easily be converted to hexadecimal by grouping bits 4 at a time and writing the equivalent hex character. Express 1001 0110 0000 11102 in hexadecimal: Example Solution Group the binary number by 4-bits starting from the right. Thus, 960E**Decimal**Hexadecimal Binary Hexadecimal Numbers 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1415 0 1 2 3 4 5 6 7 8 9 A B C D E F 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 Hexadecimal is a weighted number system. The column weights are powers of 16, which increase from right to left. { 163 162 161 160 . Column weights 4096 256 16 1 Example Express 1A2F16 in decimal. Start by writing the column weights: 4096 256 16 1 Solution 1 A 2 F16 1(4096) + 10(256) +2(16) +15(1) = 670310**Binary and Hex Conversion Games**• You must memorize the binary and hex codes for the numbers from 1 through 15. • To practice, play the Binary-Decimal and Binary Hex matching games on my Games page.**Decimal**Binary BCD BCD 0 1 2 3 4 5 6 7 8 9 10 11 12 13 1415 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 1111 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 0000 0001 0010 0011 0100 0101 Binary coded decimal (BCD) is a weighted code that is commonly used in digital systems when it is necessary to show decimal numbers such as in clock displays. The table illustrates the difference between straight binary and BCD. BCD represents each decimal digit with a 4-bit code. Notice that the codes 1010 through 1111 are not used in BCD. 0001 0001 0001 0001 0001 0001**BCD**You can think of BCD in terms of column weights in groups of four bits. For an 8-bit BCD number, the column weights are: 80 40 20 10 8 4 2 1. Question: What are the column weights for the BCD number 1000001101011001? Answer: 8000 4000 2000 1000800 400 200 10080 40 20 108 4 2 1 Note that you could add the column weights where there is a 1 to obtain the decimal number. For this case: 8000 + 200 +100 + 40 + 10 + 8 +1 = 835910**The ASCII Code**• ASCII (American Standard Code for Information Interchange) is a binary code for alphanumeric symbols. • ASCII encodes 128 symbols using 7-bits. • See Table 1-5 on page 19 (next slide) for the list of ASCII codes. • The first 32 symbols are control characters (such as Backspace, Line Feed, Form Feed), based on teletype requirements. Some of these are obsolete.

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