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') DIGITAL FUNDAMEN'I'ALS. • . I This is the first in a series of short courses that will quickly teach you the basics of digital electronics. We 'II begin by considering binary and· hexadecimal numbers. .. j • .JI I LESSON 1: BINARY DATA By Louis E. Frenzel, Jr. .1 r , ... .... I Digital logic circuits use on-off, pulse-type signals to process and communicate information. Such circuits are now found in virtually all types of electronic equipment. This series of self-instructional lessons introduces the subject of digital electronics. It will show you how digital circuits operate. What you can expect to learn in this article is this: the difference between analog and digital methods; why digital methods are used; binary data representation; converting between binary and decimal numbers; understanding hexadecimal, BCD and ASCII data; how to represent binary information with electronic signals and components; and exactly what is serial and parallel data. analog and digital. The terms analog and digital r efer to the types of signals and circuits used in electronic processes. An analog signal is one that varies smoothly and continuously. Fig.1 shows several kinds of analog signals. A constant positive DC voltage level of 6 volts is illustrated in Fig.lA. An alternating current (AC) signal known as a sinewave in shown in Fig.lB. It has CONSTANT OC VOLTAGE +6V----'/"--r---- VOLTAGE VALUE Electronic applications The three basic applications for electronics are communications, computation and control. In communications, we transmit information from one place to another by wires or radio techniques. In computation, we process data. Numerical, text and o,ther types of information are manipulated with mathematical or logic techniques to create new information. Computers, of course, are our data processors. Control refers to automating industrial and other processes. That means using electronics methods to operate equipment remotely and/or automatically. All three areas of electronics are well known and you can probably name numerous examples of each. Analog and digital There are two basic methods used in implementing electronic communications , computation, and control processes. And there are two basic methods of representing information. Those two methods are O V ' - - - - - ' - -- ----TIME (b) (a) RANDOM ANALOG SIGNAL (c) Fig. 1 - Three sample analog voltages: A, constant DC voltage typical of that produced by a voltage regulator circuit; B, sinewave signal typical of an unmodulated AM broadcast station or signal generator; and C, random analog signal that may be the plot of temperature, light intensity during a cloudy day, or just about any type of non-periodic event. NOVEMBER1987 83 tional weights as units, tens, hundreds, thousands, etc. a peak value ± 3 volts and a peak-to-peak value of 6 Each position is a successively larger power of 10: 10 volts. A randomly varying analog signal is shown in to the O power = 10° = 1; 10 to the 1st power = 10 1 Fig.lC. Although the latter may appear to be random, = 10; 10 to the 2nd power = 10 2 = 100; 10 to the 3rd power = 10' = 1000; etc. The simple illustration it could be a track of temperature during a 24-hour below shows how any decimal number is structured period, a section of a voice signal, or the rise and fall and evaluated. of a local tide. The other type of electronics signal is a digital one. Instead of a smooth, continuous Thousand Hundreds Tens Units variation, a digital signal is made up of clearly 1 9 8 5 1 X 1000 = 1000 9 X 100 = 900 8 X 10 = 80 5 X 1 = 5 defined discrete voltage or current levels with abrupt changes between them. The most 1,000 900 80 5 = 1985 + + + common type of digital signal is the two-level or binary-pulse type signal shown in Fig.2. In In digital circuits, we use binary numbers rather Fig.ZA, the signal switches between the O and + 5V levels. In Fig.2B, the two switched states are - 12 and than decimal numbers. In the binary number system + 12 volts. only two digits, 0 and 1, are used. For example, the While digital signals can have more than two binary number 1010011 represents the decimal discrete levels, typically they do not. The term digital number 83. The digits O and 1 are called binary digits is virtually synonymous with the term binary which or bits. Like the decimal number system, the binary implies two levels. system uses a positional or weighted method. Instead of weights of some power of 10, the position weights in Representing information the binary number as some power of 2. Thus we have Digital and analog signals typically represent infor2 to the O power = 2° = 1; 2 to the 1st power = 21 = mation to be communicated or processed. For exam2; 2 to the 2nd power = Z2 = 4; 2 to the 3rd power = ple, the analog voice signal generated by a microphone Z3 = 8; etc. Note that each successively higher weight might be modulated and transmitted by radio. Or the is twice that of the preceding weight. binary input from a keyboard may be processed by a The structure of a typical binary number is shown digital computer to enter your savings deposit. Those below. signals, representing information (data), are then processed to accomplish some useful end result. Analog Weight 64 16 4 2 1 32 8 1 Number 1 1 0 1 signals are processed by analog (linear) circuits. 0 0 LSB MSB Binary data is processed by digital logic circuits. At one time, virtually all electronic signals and pro64 + 0 + 16 + 0 + 0 + 2 + 1 = 83 cesses were analog. However, with the development of the digital computer, digital methods became more Notice that the binary number is usually made up of popular and widely used. Then, semiconductor a number of bits; in this case, eight. Each bit may be technology gave us digital integrated circuits and the binary O or binary 1. The weight of each position is inmicroprocessor, both of which have revoltionised elecdicated. Note particularly the least significant bit tronics technology. Today, digital methods are prefer(LSB) with the lowest position weight and the most red because of their ease of implementation, low cost, significant bit (MSB) with the highest position weight. reliability and overall effectiveness. While digital The question is: how do you determine what decimal techniques will never replace analog techniques comquantity is represented by a given binary number? pletely, the use of digital techniques has grown continuously over the years and today virtually dominates Converting a binary number to in most electronics applications. Decimal verses binary numbers The information or data to be communicated, processed, or used for control purposes is usually numerical in nature. For that reason, the main language of digital techniques involves Weight 32 16 numbers that can also Number 1 1 represent letters of the 1 X 32 = 32 X 16 = 16 alpha bet and even 32 t16 + special control features. You are familiar with the decimal number system where we use the digits O through 9 in various combinations to represent any quantity. The decimal number system is based upon a method of giving numerical weights to each position or digit in the number. Recall that we usually refer to those posi84 SILICON CHIP its decimal value Evaluating a binary number means determining its decimal value. The process is similar to that used in evaluating any other decimal number. The illustration below shows what we mean. 8 1 X 8 = 8 0 8 + X 4 2 1 0 4 =0 1 2 =2 0 1=0 0 X +· 2 0 + X 0 -- 58 To determine the decimal value of a given binary number, all you do is multiply each bit by its position weight, then sum all those values. Looking closely at the process above, you can see that those bit positions with a zero in them actually have no effect on the outcome. For that reason, they can be ignored. You can OV OFF ON OFF -12V -- W 00 0000 0001 0010 0011 4 5 0100 0101 0110 0111 6 7 Fig.2 - Two commonly used digital signals used in electronic circuits. The left one (A) is from a singleended output such as from a 4000 chip series; and B, the output from a balanced op amp that uses ± 12V DC rails. quickly evaluate the binary number by simply adding up the weights of those positions that contain a binary 1 bit. The secret is in remembering the weight of each position, and that's easy. Converting a decimal number to its binary equivalent Another procedure that you will find handy is that for converting a decimal number into its binary equivalent. The process is essentially that of dividing the original number by two, then dividing the resulting quotient by two continuously until a quotient of zero is obtained. The remainders resulting from each of those divisions form the binary number. Division Remainder 84 .,_ 42-'21 -'10 _,_ 0 LSB 0 1 0 1 0 5 .,_ 2 = 2 2 _,_ 2 = 1 1 .,_ 2 = 0 Binary 0 1 2 3 Therefore, 84 = 1010100 1 MSB Maximum decimal value A binary number, or binary word as it is sometimes called, usually consists of a fixed number of bits when used within one confined system. With that number of bits you can represent a certain maximum value. The same is true of decimal numbers. With a given number of digits, some maximum value can be represented. For example, with four digits, the maximum decimal value is 9999. With a 4-bit binary number. the maximum value is 1111. The question is: what's the maximum decimal value for a given number of binary bits? This value can be computed using the simple formula shown below: Hexadecimal Binary 0 1 2 0000 0001 0010 0011 0100 0101 0110 0111 6 7 1 1100 1101 1110 1111 To represent larger and larger decimal values, binary numbers with more bits must be used. And, as the binary numbers get larger, they become increasingly difficult to work with. For example, it takes 20 bits to respresent one million (1,0448,576 to be exact). It's tough enough to remember a long decimal number, but just imagine the problem of remembering a very long binary number. That task is made easier by the use of a special shorthand known as hexadecimal notation which uses hexadecimal numbers. Hex means six and, of course, decimal means ten; therefore hexadecimal means sixteen. Hexadecimal refers to a special notation as well as a number system using a total of 16 digits. Those digits are the decimal numbers 1 through 9, and the letters A through F. Each digit corresponds to its equivalent 4-bit binary code as shown in Fig.4. The idea is to use the hex digit corresponding to each 4-bit where M is the maximum decimal value and n is the number of bits. To illustrate the use of the formula, let's determine the maximum decimal value you can represent with 4 bits. This is done as shown below: - 12 13 14 15 Hexadecimal notation 4 5 24 10 11 1000 1001 1010 1011 word with their decimal equivalents. There are sixteen values, 0 through to a maximum of 15. Remember that 0 (zero) is a number and it is one of 16 values that can be represented by a 4-bit binary number. Eight bits is a very common binary word size. With 8 bits, you can represent decimal values up to 28 - 1 = 255 . 8-bit words or numbers are so widely used that they have been given a special name. An 8-bit number or word is called a byte. You will also hear the term nibble to refer to 4-bit words. 3 = Binary Fig.3 - The decimal/binary equivalents are listed here for the first 16 numbers. Keep in mind that 0 (zero) is a number. M = 2" - 1 M Decimal 8 9 ON ~TIME 2 = 42 2 = 21 2 = 10 2 = 5 Decimal = (2x2x2x2) - 1 = 16 - 1 = 15 Fig.3 shows all possible combinations of a 4-bit Hexadecimal. 8 9 A B C D E F Binary 1000 1001 1010 1011 1100 1101 1110 1111 Fig.4 - The hexadecimal/binary equivalents are listed here for the first 16 numbers. Compare this illustration to that of Fig.3. When you use the hexadecimal number system for a short while, you will begin to appreciate the convenience of the system. NOVEMBER 1987 85 segment of a long binary number. The result is a shorter hexadecimal number that is far easier to remember and apply. To convert a binary number into a hexadecimal number, all you do is divide the long binary number into 4-bit segments starting with the LSB on the far right. Then, you replace each of those 4-bit segments with the corresponding hex digit from Fig.4. The result is illustrated below. B 1 ~ 0 ~ 0 MSB B t1 1 UP (1) DOWN (D) 1 LSB +5V MSB 0 (DV) 0 (DY) 1 (+5V) LSB 1011 /0001 /0111 /0010/1101 B 1 7 2 D Changing a hexadecimal number back into its binary equivalent is also easy. You simply reverse the above process; ie, you replace each hexadecimal digit with its binary equivalent and string all of the resulting bits together as shown below. 6 F 9 0 5 0110/1111 /1001 /0000/0101 Binary coded decimal (BCD) Besides the standard binary notation for representing a decimal number, some special variations are also widely used. The most common is binary coded decimal (BCD). The BCD system is essentially a hybrid of both the binary and decimal systems. It uses binary digits, but a separate 4-bit group is used to represent each decimal digit individually. The BCD code is the same as the first ten digits (0 to 9) of the hexadecimal code in Fig.4. To represent a given binary coded decimal value, you simply use the 4-bit group representing each digit. An example is given below using the decimal number 4891: 4 8 9 1 0100 1000 1001 0001 A space is left between each 4-bit group to denote separate digits. BCD is a widely used method as it greatly simplifies the conversion process between binary and decimal. It is also an aid in improving communications between man and machine. Where a human operator must interface with a piece of communications equipment, BCD is normally employed. Keyboards generally produce BCD outputs. BCD information from a piece of electronic equipment is normally used to drive the 7-segment decimal displays that are so popular. ASCII A special form of BCD is widely used in computers. Known as the American Standard Code of Information Interchange (ASCII, pronounced ass-key), it normally uses 7-bits to represent not only the decimal digits Oto 9, but also letters of the alphabet (both upper and lower case), punctuation marks, and special symbols. Some examples of ASCII designations are shown below. 8 L J ? Bell 86 011 100 110 011 000 1000 (Last 4-bits same as BCD) 1100 1010 1111 0 111 (This code rings a bell or sounds a tone.) SILICON CHIP 1 (+5V) • 1 (+5V) • .,. Fig.5 - A simple manual switching circuit can be constructed and used to demonstrate binary data for decimal numbers O to 31. The ASCII code is widely used in computers. It is the main code used in communicating information between computers and peripheral devices. For example, virtually all printers produce hard copy output from ASCII input supplied by the computer. ASCII coded data is also what is normally transmitted and received by a modem in digital communications. Representing binary numbers with hardware The reason for using the binary number system in digital equipment is that it is easier to implement binary electronic circuits than it is decimal circuits. Decimal circuits would have to represent at least 10 states. With binary, only two states are required. As a result, any electronic component that can assume two states can be used for binary representation. The result is smaller, simpler, cheaper and faster circuits. The most obvious component to represent a bit is a switch. A switch can be off or on and, therefore, can represent O and 1. Fig.5 shows how a group of slide switches is used to produce binary data. The number being displayed on those switches is 10011 , whose decimal equivalent is 19. The illustration also shows what the schematic diagram may look like. When the slide switch is down, it is closed. The voltage at the output, therefore, is 0 volts or ground potential. That typically represents a binary O (sometimes referred to as a logic low). When the switch is up, it is open. As a result, the output is + 5 volts as seen through the resistor. This represents a binary 1 (or a logic high). Another obvious choice for a component to repre' I , ON: 1 - Q - , OFF:O '' 0 -a- o -a- o -a.·:- o I I 0 = 42 Fig.6 - A six-unit light emitting diode (LED) display can be used to display binary data for decimal numbers from O to 63. The most significant bit is at the display left side. FOUR BITS OF PARALLEL DATA 0 '""' SOURCE OF DATA I I I I I I 0 DESTINATION OF DATA ov- 1 ...., 1. +sv- 1 Fig. 7 - 4-bits of parallel data from a circuit like that in Fig.5 can be transmitted over four lines at the same time. The destination could be another chip on the same circuit board, a remote printer, or some other devices. sent binary data is a simple light. Both incandescent lamps and light emitting diodes (LEDs) are used to display binary information. An off (unlit) display represents a binary 0, while an on (lit) display respresents a binary 1. Fig.6 shows how a typical binary LED display might look. The key component in any electronic circuit is the transistor which is used in digital circuits as a switch. A transistor can be on (conducting), or off (nonconducting). Those are natural conditions representing binary 0 and binary 1 states. Parallel and serial data Binary data in digital circuits is generated, processed, displayed, or communicated. There are two ways in which those things are done: parallel and serial. Parallel binary data is where all bits of a word are generated, processed, transmitted or displayed simultaneously. The data generated by the switches in Fig.5 and that displayed in Fig.6 are both examples of parallel binary data. All bits of the word occur at the same time and can be transmitted from one place to another as shown in Fig. 7. t - START BIT If.-ONE PERIOD ---l-TIME STOP Fig. 8 - An 8-bit serial binary word displayed against time. The other form of binary data is serial. Serial binary data is transmitted or processed one bit at a time. The bits occur sequentially and, therefore, each is handled separately in order. A serial data word is shown in Fig.8. The binary 0's and 1's are represented by voltage levels. Note that each bit occurs for a fixed length of time. If each bit lasts one millisecond, then it will take a total of 8 milliseconds to transmit and process one byte. As you can see, the main disadvantage of serial data is the long time required to transmit or process it. On the other hand, serial data is far less expensive to deal with. Only one set of processing circuits is required to transmit it from one place to another. Despite its low-speed disadvantage, serial data is widely used. It is perfectly suitable for many digital applications. In Lesson 2 next month, we'll take a look at the five basic digital logic elements and learn how to use their truth tables. Reproduced from Hands-On Electronics by arrangement. Gernsback Publications, USA. © SHORT QUIZ ON DIGIT AL FUNDAMENTALS 1 . The three primary eletronics applications are _ _ _ _ _ ,and _ __ __ 2 . a. Smooth , continuous signals are called 5 . An eight-bit number is called a _ _ _ _ _ __ 6 . Write the BCD equivalent of 2805 . - - - - - - - - -- the number ---- b. Digital signals usually have _ _ (how many?) levels. 7 . The special code used to transmit letters as well as numbers is called _ _ _ __ _ _ _ _ __ 3 . Refer to the LED binary display above . What decimal number is represented? _ _ __ _ __ 8 . The maximum decimal value you can represent with 12 bits is _ _ _ _ _ _ _ _ _ _ _ __ 0 MSB -QLSB 4. a. If binary O = O volt and binary 1 = +6 volt, write the binary output voltage levels equivalent to the decimal number 207 . MSB ____ ,____ , _ __ ,___ ,___ ,_ _ _ ,_ _ _ ,_ __ ,LSB. b. The above decimal number expressed as a hexadecimal number is _ _ _ _ _ _ _ _ __ 9. Which method of processing and transmission of binary data is slower? _ __ ____ parallel _ _ _ __ __serial. repas 960t = •- ·e 960t = • - .. c: :geot ·e .o .o 0000 000 ~ 11:::>S'v' . L 0 ~00 ·g a1Aq ·g ::I:) ·q :••• wo •• = 8S7 ' 9+ '9+ '9+ '9+ ·o ·o •9+ •9+ ssv-i ·e (I-ewpap) 69 • = (AJBU!Q) .oo .o •O • ·v ·s ·c: OMI ·q :BoIBUB ·e iOJjUO::l 'UO!IBlndwo::i 'SUO!JB::l!Unwwo::i . • NOVEMBER 1987 87