Objectives After completing this experiment, you will be able to Convert binary or binary coded decimal (BCD) numbers to decimal. Construct a portion of a digital system that decodes a BCD

number and displays it on a seven-segment display. Troubleshoot the circuit for simulated faults. Materials Needed Four LEDs 7447A BCD/decimal decoder MAN72 seven-segment display Four-position DIP switch Resistors: eleven 330 £2, one 1.0 k For Further Investigation: Additional LED One 330 2 resistor Summary of Theory The number of symbols in a number system is called the base, or radix, of that system. The dec- imal number system uses ten counting symbols, the digits 0 through 9, to represent quantities. Thus it is a base ten system. In this system, we represent quantities larger than 9 by using positional weight- ing of the digits. The position, or column, that a digit occupies indicates the weight of that digit in determining the value of the number. The base 10 number system is a weighted system because each column has a value associated with it. Digital systems use two states to represent quantities and thus are binary in nature. The binary counting system has a radix of two and uses only the digits 0 and 1. (These are often called bits, which is a contraction of BInary digiT). It too is a weighted counting system, with each column value worth twice the value of the column to the immediate right. Because binary numbers have only two digits, large numbers expressed in binary require a long string of Os and 1s. Other systems, which are related to binary in a simple way, are often used to simplify these numbers. These systems include octal, hexa- decimal, and BCD. The octal number system is a weighted number system using the digits 0 through 7. The column values in octal are worth 8 times that of the column to the immediate right. You convert from binary to octal by arranging the binary number in groups of 3 bits, starting at the binary point, and writing the octal symbol for each binary group. You can reverse the procedure to convert from octal to binary. Simply write an equivalent 3-bit binary number for each octal character. The hexadecimal system is a weighted number system using 16 characters. The column values in hexadecimal (or simply hex) are worth 16 times that of the column to the immediate right. The characters are the numbers 0 through 9 and the first six letters of the alphabet, A through F. Letters were chosen because of their sequence, but remember that they 21/nare used to indicate numbers, not letters. You convert binary numbers to hexadecimal numbers by arranging the binary number into 4-bit groups, start- ing at the binary point. Then write the next symbol for each group of 4 bits. You convert hex numbers to binary by reversing the procedure. That is, write an equivalent 4-bit binary number for each hexadeci- mal character. The BCD system uses four binary bits to rep- resent each decimal digit. It is a convenient code because it allows ready conversion from base ten to a code that a machine can understand; however, it is wasteful of bits. A 4-bit binary number could repre- sent the numbers 0 to 15, but in BCD it represents only the quantities 0 through 9. The binary repre- sentations of the numbers 10 through 15 are not used in BCD and are invalid. The conversion of BCD to a form that can be read by humans is a common problem in digital systems. A familiar display is called the seven- segment display, which is used in many digital ap- plications such as clocks. A basic seven-segment display is described in this experiment with the instructions for wiring it. Later, in the text, the inner workings of the decoder and seven-segment display are explored. The block diagram for the tablet-bot- tling system that was introduced in Chapter 1 is an example of a small system that used a BCD to seven-segment conversion circuit (see Figure 1-27 of the text). It is used in both the on-site display and the remote display portions of that system. You will construct a simplified version of the display for this experiment. 21 Procedure 1. Take a moment to review "Circuit Wiring" in the Introduction before constructing the circuit in this experiment. The pin numbers for the integrated circuits (ICs) in this and succeeding experiments are not shown; pin numbers may be found on the data sheets in Appendix A or on the manufacturer's website. It is a good idea to write the pin numbers directly on the schematic before you begin wiring. 2. Begin by constructing the circuit shown in Figure 3-1, which will represent a BCD input. After wiring the circuit, connect power and test each switch to see that it lights an LED. 3. Remove power and add the circuit shown in Figure 3-2. An example of the wiring is shown in Figure 3-3. If you have not already done so, write the pin numbers on the schematic. The pin numbers for the MAN72 display are shown in Figure 3-4.* Note that the 7447A has 16 pins, but the MAN72 has only 14 pins. Before applying power, check that you have connected a 330 2 current-limiting resistor between each output of the decoder and the input to the MAN72. Connect the Lamp test, BI/RBO, and RBI inputs through a 1.0 k2 resistor to +5.0 V. This is a pull-up resistor, used to assure a solid logic HIGH is present at these inputs. *Pin numbers for the 7447A decoder can be found in Appendix A./nEvaluation and Review Questions 1. Assume the switches in Figure 3-2 are set for a binary 1000, but the display shows a zero. What are three possible causes for this error? 2. Looking at the possible causes for an error from Question 1, how would you go about troubleshooting the problem? 3. Suppose that the BI/RBO input line was shorted to ground on the 7447A decoder and all other input lines were okay. Looking at the function table for the 7447A in Appendix A, determine the effect this would have on the display. 4. Explain the difference between binary and BCD. 5. Convert each number shown into the other bases: Binary 01001100 Octal 304 Hexadecimal E6 Decimal 57 BCD 0100 1001 6. a. The decimal number 85 is equal to 125 in a certain other number system. What is the base of the other system? b. The decimal number 341 is equal to 155 in a certain other number system. What is the base of the other system?