(Solution Manual) Digital Fundamentals

Floyd, 11

General Science

Solution Manual

11th Edition

• $15.00 $50.00

---

Description

Solution Manual for Digital Fundamentals, The downloadable file consists of 319 pages, and the total size of the file is 3.64 MB. Purchase now only for highly discounted price.

Author(s): Floyd

---

---

Study Note Preview

Solutions Manual for Digital Fundamentals, 11e Thomas Floyd (All Chapters ) PART 1 Problem Solutions Chapter 1 2 CHAPTER 1 INTRODUCTORY CONCEPTS Section 1-1 Digital and Analog Quantities 1. Digital data can be transmitted and stored more efficiently and reliably than analog data. Also, digital circuits are simpler to implement and there is a greater immunity to noisy environments. 2. Pressure is an analog quantity. 3. A clock, a thermometer, and a speedometer can have either an analog or a digital output. Section 1-2 Binary Digits, Lo gic Levels, and Digital Waveforms 4. In positive logic, a1 is represented by a HIGH level and a 0 by a LOW level. In negative logic, a 1 is represented by a LOW level, and a 0 by a HIGH level. 5. HIGH = 1; LOW = 0. See Figure 1-1. 6. A 1 is a HIGH and a 0 is a LOW: (a) HIGH, LOW, HIGH, HIGH, HIGH, LOW, HIGH (b) HIGH, HIGH, HIGH, LOW, HIGH, LOW, LOW, HIGH Chapter 1 37. See Figure 1-2. 8. T = 4 ms. See Figure 1-3. 9. f = ms 41 1=T = 0.25 kHz = 250 Hz 10. The waveform in Figure 1-61 is periodic because it repeats at a fixed interval. 11. tW = 2 ms; T = 4 ms % duty cycle =  = ms 4ms 2100 W Tt100 = 50% 12. See Figure 1-4. PWt2.7 s μ Ampl = 10 V Chapter 1 4 13. Each bit time = 1 μs Serial transfer time = (8 bits)(1 μs/bit) = 8 μs Parallel transfer time = 1 bit time = 1 μs 14. 11 3.5 GHzTf = 0.286 ns Section 1-3 Basic Logic Functions 15. ONL = SW1 + SW2 + SW1  SW2 16. An AND gate produces a HIGH output only when all of its inputs are HIGH. 17. AND gate. See Figure 1-5. 18. An OR gate produces a HIGH output when either or both inputs are HIGH. An exclusive-OR gate produces a HIGH if one input is HIGH and the other LOW. Section 1-4 Combinational and Sequential Logic Functions 19. See Figure 1-6. Chapter 1 520. T = kHz 101 = 100 μs Pulses counted = s 100ms 100 μ = 1000 21. See Figure 1-7. Section 1-5 Introduction to Programmable Logic 22. The following do not describe PLDs: VHDL, AHDL 23. (a) SPLD: Simple Programmable Logic Device (b) CPLD: Complex Programmable Logic Device (c) HDL: Hardware Description Language (d) FPGA: Field-Programmable Gate Array (e) GAL: Generic Array Logic 24. (a) Design entry: The step in a programmable logic design flow where a description of the circuit is entered in either schematic (graphic) form or in text form using an HDL. (b) Simulation: The step in a design flow where the entered design is simulated based on defined input waveforms. (c) Compilation: A program process that controls the design flow process and translates a design source code to object code for testing and downloading. (d) Download: The process in which the design is transferred from software to hardware. 25. Place-and-route or fitting is the process where the logic structures described by the netlist are mapped into the actual structure of the specific target device. This results in an output called a bitstream. Section 1-6 Fixed-Function Logic Devices 26. Circuits with complexities of from 100 to 10,000 equivalent gates are classified as large scale integration (LSI). 27. The pins of an SMT are soldered to the pads on the surface of a pc board, whereas the pins of a DIP feed through and are soldered to the opposite si de. Pin spacing on SMTs is less than on DIPs and therefore SMT packages are physically smaller and require less surface area on a pc board. Chapter 1 6 28. See Figure 1-8. Section 1-7 Test and Measurement Instruments 29. Amplitude = top of pulse minus base line V = 8 V − 1 V = 7 V 30. Amplitude = (3 div)(2 V /div) = 6 V. 31. T = (4 div)(2 ms/div) = 8 ms f = 11 8 msT = 125 Hz 32. Record length = (Acquisition time)(sample rate) = (2 ms) 12 Msamples/s = 24 ksamples Section 1-8 Introduction to Trouble Shooting 33. Troubleshooting is the process of recognizing, isolating, and correcting a fault or failure in a system. 34. In the half-splitting method, a point half way between the input and output is checked for the presence or absence of a signal. 35. In the signal-tracing method, a signal is tracked as it progresses through a system until a point is found where the signal disappears or is incorrect. 36. In signal subsitution, a generated signal replaces the normal input signal of a system or portion of s system. In signal injection a generated signal is injected into the system at a point where the normal signal has been determined to be faulty or missing. 37. When a failure is reported, determine when and how it failed and what are the symptoms. Chapter 1 738. No output signal can be caused by no dc power, no input signal, or a short or open that prevents the signal from getting to the output. 39. An incorrect output can be caused by an incorrect dc supply voltage, improper ground, incorrect component value, or a faulty component. 40. Some types of obvious things that you look for when a system fails are visible faults such as shorted wires, solder splashes, wire clippings, bad or open connections, burned components, Also look for a signal that is incorrect in terms of amplitude shape, or frequency or the absence of a signal. 41. To isolate a fault in a system, apply half-splitting or signal tracing. 42. Two common troubleshooting instruments are the oscilloscope and the DMM. 43. When a fault has been isolated to a particular circuit board, the options are to repair the board or replace the board with a known good board. 8 CHAPTER 2 NUMBER SYSTEMS, OPERATIONS, AND CODES Section 2-1 Decimal Numbers 1. (a) 1386 = 1 × 103 + 3 × 102 + 8 × 101 + 6 × 100 = 1 × 1000 + 3 × 100 + 8 × 10 + 6 × 1 The digit 6 has a weight of 100 = 1 (b) 54,692 = 5 × 104 + 4 × 103 + 6 × 102 + 9 × 101 + 2 × 100 = 5 × 10,000 + 4 × 1000 + 6 × 100 + 9 × 10 + 2 × 1 The digit 6 has a weight of 102 = 100 (c) 671,920 = 6 × 105 + 7 × 104 + 1 × 103 + 9 × 102 + 2 × 101 + 0 × 100 = 6 × 100,000 + 7 × 10,000 + 1 × 1000 + 9 × 100 + 2 × 10 + 0 × 1 The digit 6 has a weight of 105 = 100,000 2. (a) 10 = 101 (b) 100 = 102 (c) 10,000 = 104 (d) 1,000,000 = 106 3. (a) 471 = 4 × 102 + 7 × 101 + 1 × 100 = 4 × 100 + 7 × 10 + 1 × 1 = 400 + 70 + 1 (b) 9,356 = 9 × 103 + 3 × 102 + 5 × 101 + 6 × 100 = 9 × 1000 + 3 × 100 + 5 × 10 + 6 × 1 = 9,000 + 300 + 50 + 6 (c) 125,000 = 1 × 105 + 2 × 104 + 5 × 103 = 1 × 100,000 + 2 × 10,000 + 5 × 1000 = 100,000 + 20,000 + 5,000 4. The highest four-digit decimal number is 9999. Section 2-2 Binary Numbers 5. (a) 11 = 1 × 21 + 1 × 20 = 2 + 1 = 3 (b) 100 = 1 × 22 + 0 × 21 + 0 × 20 = 4 (c) 111 = 1 × 22 + 1 × 21 + 1 × 20 = 4 + 2 + 1 = 7 (d) 1000 = 1 × 23 + 0 × 22 + 0 × 21 + 0 × 20 = 8 (e) 1001 = 1 × 23 + 0 × 22 + 0 × 21 + 1 × 20 = 8 + 1 = 9 (f) 1100 = 1 × 23 + 1 × 22 + 0 × 21 + 0 × 20 = 8 + 4 = 12 (g) 1011 = 1 × 23 + 0 × 22 + 1 × 21 + 1 × 20 = 8 + 2 + 1 = 11 (h) 1111 = 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20 = 8 + 4 + 2 + 1 = 15 Chapter 2 9 6. (a) 1110 = 1 × 23 + 1 × 22 + 1 × 21 = 8 + 4 + 2 = 14 (b) 1010 = 1 × 23 + 1 × 21 = 8 + 2 = 10 (c) 11100 = 1 × 24 + 1 × 23 + 1 × 22 = 16 + 8 + 4 = 28 (d) 10000 = 1 × 24 = 16 (e) 10101 = 1 × 24 + 1 × 22 + 1 × 20 = 16 + 4 + 1 = 21 (f) 11101 = 1 × 24 + 1 × 23 + 1 × 22 + 1 × 20 = 16 + 8 + 4 + 1 = 29 (g) 10111 = 1 × 24 + 1 × 22 + 1 × 21 + 1 × 20 = 16 + 4 + 2 + 1 = 23 (h) 11111 = 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20 = 16 + 8 + 4 + 2 + 1 = 31 7. (a) 110011.11 = 1 × 25 + 1 × 24 + 1 × 21 + 1 × 20 + 1 × 2−1 + 1 × 2−2 = 32 + 16 + 2 + 1 + 0.5 + 0.25 = 51.75 (b) 101010.01 = 1 × 25 + 1 × 23 + 1 × 21 + 1 × 2−2 = 32 + 8 + 2 + 0.25 = 42.25 (c) 1000001.111 = 1 × 26 + 1 × 20 + 1 × 2−1 + 1 × 2−2 + 1 × 2−3 = 64 + 1 + 0.5 + 0.25 + 0.125 = 65.875 (d) 1111000.101 = 1 × 2 6 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 2−1 + 1 × 2−3 = 64 + 32 + 16 + 8 + 0.5 + 0.125 = 120.625 (e) 1011100.10101 = 1 × 2 6 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 2−1 + 1 × 2−3 + 1 × 2−5 = 64 + 16 + 8 + 4 + 0.5 + 0.125 + 0.03125 = 92.65625 (f) 1110001.0001 = 1 × 26 + 1 × 25 + 1 × 24 + 1 × 20 + 1 × 2−4 = 64 + 32 + 16 + 1 + 0.0625 = 113.0625 (g) 1011010.1010 = 1 × 26 + 1 × 24 + 1 × 23 + 1 × 21 + 1 × 2−1 + 1 × 2−3 = 64 + 16 + 8 + 2 + 0.5 + 0.125 = 90.625 (h) 1111111.11111 = 1 × 26 + 1 × 25 + 1 × 24 + 1 × 23 + 1 × 22 + 1 × 21 + 1 × 20 + 1 × 2−1 + 1 × 2−2 + 1 × 2−3 + 1 × 2−4 + 1 × 2−5 = 64 + 32 + 16 + 8 + 4 + 2 + 1 + 0.5 + 0.25 + 0.125 + 0.0625 + 0.03125 = 127.96875 8. (a) 22 − 1 = 3 (b) 23 − 1 = 7 (c) 24 − 1 = 15 (d) 25 − 1 = 31 (e) 26 − 1 = 63 (f) 27 − 1 = 127 (g) 28 − 1 = 255 (h) 29 − 1 = 511 (i) 210 − 1 = 1023 (j) 211 − 1 = 2047 9. (a) (2 4 − 1) < 17 < (25 − 1); 5 bits (b) (25 − 1) < 35 < (26 − 1); 6 bits (c) (25 − 1) < 49 < (26 − 1); 6 bits (d) (26 − 1) < 68 < (27 − 1); 7 bits (e) (26 − 1) < 81 < (27 − 1); 7 bits (f) (26 − 1) < 114 < (27 − 1); 7 bits (g) (27 − 1) < 132 < (28 − 1); 8 bits (h) (27 − 1) < 205 < (28 − 1); 8 bits Chapter 2 10 10. (a) 0 through 7: 000, 001, 010, 011, 100, 101, 110, 111 (b) 8 through 15: 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111 (c) 16 through 31: 10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110, 11111 (d) 32 through 63: 100000, 100001, 100010, 100011, 100100, 100101, 100110, 100111, 10100, 101001, 101010, 101011, 101100, 101101, 101110, 101111, 110000, 110001, 110010, 110011, 110100, 110101, 110110, 110111, 111000, 111001, 111010, 111011, 111100, 111101, 111110, 111111 (e) 64 through 75: 1000000, 1000001, 1000010, 1000011, 1000100, 1000101, 1000110, 1000111, 1001000, 1001001, 1001010, 1001011 Section 2-3 Decimal- to-Binary Conversion 11. (a) 10 = 8 + 2 = 23 + 21 = 1010 (b) 17 = 16 + 1 = 24 + 20 = 10001 (c) 24 = 16 + 8 = 24 + 23 = 11000 (d) 48 = 32 + 16 = 25 + 24 = 110000 (e) 61 = 32 + 16 + 8 + 4 + 1 = 25 + 24 + 23 + 22 + 20 = 111101 (f) 93 = 64 + 16 + 8 + 4 + 1 = 26 + 24 + 23 + 22 + 20 = 1011101 (g) 125 = 64 + 32 + 16 + 8 + 4 + 1 = 26 + 25 + 24 + 23 + 22 + 20 = 1111101 (h) 186 = 128 + 32 + 16 + 8 + 2 = 27 + 25 + 24 + 23 + 21 = 10111010 12. (a) 0.32 ≅ 0.00 + 0.25 + 0.0625 + 0.0 + 0.0 + 0.0078125 = 0.0101001 (b) 0.246 ≅ 0.0 + 0.0 + 0.125 + 0.0625 + 0.03125 + 0.015625 = 0.001111 (c) 0.0981 ≅ 0.0 + 0.0 + 0.0 + 0.0625 + 0.03125 + 0.0 + 0.0 + 0.00390625 = 0.0001101 Chapter 2 1113. (a) 215 = 7, R = 1( LSB) 27 = 3, R = 1 23 = 1, R = 1 21 = 0, R = 1 (MSB) (d) 234 = 17, R = 0 (LSB) 217 = 8, R = 1 28 = 4, R = 0 24 = 2, R = 0 22 = 1, R = 0 21 = 0, R = 1 (MSB) (g) 265 = 32, R = 1 (LSB) 232 = 16, R = 0 216 = 8, R = 0 28 = 4, R = 0 24 = 2, R = 0 22 = 1, R = 0 21 = 0, R = 1 (MSB) (b) 221= 10, R = 1 (LSB) 210= 5, R = 0 25= 2, R = 1 22= 1, R = 0 21= 0, R = 1 (MSB) (e) 240= 20, R = 0 (LSB) 220= 10, R = 0 210= 5, R = 0 25= 2, R = 1 22= 1, R = 0 21 = 0, R = 1 (MSB) (h) 273 = 36, R = 1 (LSB) 236 = 18, R = 0 218 = 9, R = 0 29 = 4, R = 1 24 = 2, R = 0 22 = 1, R = 0 21 = 0, R = 1 (MSB) (c) 228 = 14, R = 0 (LSB) 214 = 7, R = 0 27 = 3, R = 1 23 = 1, R = 1 21 = 0, R = 1 (MSB) (f) 259 = 29, R = 1 (LSB) 229 = 14, R = 1 214 = 7, R = 0 27 = 3, R = 1 23 = 1, R = 1 21 = 0, R = 1 (MSB) Chapter 2 12 14. (a) 0.98 × 2 = 1.96 1 (MSB) (b) 0.347 × 2 = 0.694 0 (MSB) 0.96 × 2 = 1.92 1 0.694 × 2 = 1.388 1 0.92 × 2 = 1.84 1 0.388 × 2 = 0.776 0 0.84 × 2 = 1.68 1 0.776 × 2 = 1.552 1 0.68 × 2 = 1.36 1 0.552 × 2 = 1.104 1 0.36 × 2 = 0.72 0 0.104 × 2 = 0.208 0 continue if more accuracy is desired 0.208 × 2 = 0.416 0 0.111110 continue if more accuracy is desired 0.0101100 (c) 0.9028 × 2 = 1.8056 1 (MSB) 0.8056 × 2 = 1.6112 1 0.6112 × 2 = 1.2224 1 0.2224 × 2 = 0.4448 0 0.4448 × 2 = 0.8896 0 0.8896 × 2 = 1.7792 1 0.7792 × 2 = 1.5584 1 continue if more accuracy is desired 0.1110011 Section 2-4 Binary Arithmetic 1000111 (a) +15. 1101110111 (d) + 1001010 (b) + 111001011001 (e) + 1000011101 (c) + 1100010111101 (f) + 100111 (a) −16. 101100111110 (d) − 001100101 (b) − 001110011100 (e) − 001101110 (c) − 000111011111010 (f) − Chapter 2 13100111111111 (a) ×17. 10101001110111010000110111011101 (e) × 100010000010100 (b) × 10110110111011100000111011011110 (f) × 100011111000111101111 (c) × 1101101001100100001101001 (d) × 18. (a) 10100 = 010 (b) 00111001 = 0011 (c) 01001100 = 0011 Section 2-5 Complements of Binary Numbers 19. Zero is represented in 1’s complement as all 0’s (for +0) or all 1’s (for 0). 20. Zero is represented by all 0’s only in 2’s complement. 21. (a) The 1’s complement of 101 is 010. (b) The 1’s complement of 110 is 001. (c) The 1’s complement of 1010 is 0101. (d) The 1’s complement of 11010111 is 00101000. (e) The 1’s complement of 1110101 is 0001010. (f) The 1’s complement of 00001 is 11110. 22. Take the 1’s complement and add 1: (a) 01 + 1 = 10 (b) 000 + 1 = 001 (c) 0110 + 1 = 0111 (d) 0010 + 1 = 0011 (e) 00011 + 1 = 00100 (f) 01100 + 1 = 01101 (g) 01001111 + 1 = 01010000 (h) 11000010 + 1 = 11000011 Section 2-6 Signed Numbers 23. (a) Magnitude of 29 = 0011101 (b) Magnitude of 85 = 1010101 + 29 = 00011101 −85 = 11010101 (c) Magnitude of 100 10 = 1100100 (d) Magnitude of 123 = 1111011 +100 = 01100100 −123 = 11111011 Download Software files link below https://www.mediafire.com/fil e/e4khehl0p7zqtw2/SM+(Extra +Files)+Digital+Fundamentals,+ 11e+Thomas+L+Floyd.zip/file Chapter 2 14 24. (a) Magnitude of 34 = 0100010 (b) Magnitude of 57 = 0111001 −34 = 11011101 +57 = 00111001 (c) Magnitude of 99 = 1100011 (d) Magnitude of 115 = 1110011 −99 = 10011100 +115 = 01110011 25. (a) Magnitude of 12 = 1100 (b) Magnitude of 68 = 1000100 +12 = 00001100 −68 = 10111100 (c) Magnitude of 101 10 = 1100101 (d) Magnitude of 125 = 1111101 +101 10 = 01100101 −125 = 10000011 26. (a) 10011001 = −25 (b) 01110100 = +116 (c) 10111111 = −63 27. (a) 10011001 = −(01100110) = −102 (b) 01110100 = +(1110100) = +116 (c) 10111111 = −(1000000) = −64 28. (a) 10011001 = −(1100111) = −103 (b) 01110100 = +(1110100) = +116 (c) 10111111 = −(1000001) = −65 29. (a) 0111110000101011 → sign = 0 1.11110000101011 × 2 14 → exponent = 127 + 14 + 141 = 10001101 Mantissa = 11110000101011000000000 01000110111110000101011000000000 (b) 100110000011000 → sign = 1 1.10000011000 × 211 → exponent = 127 + 11 = 138 = 10001010 Mantissa = 11000001100000000000000 11000101011000001100000000000000 30. (a) 11000000101001001110001000000000 Sign = 1 Exponent = 10000001 = 129 − 127 = 2 Mantissa = 1.01001001110001 × 22 = 101.001001110001 −101.001001110001 = −5.15258789 (b) 01100110010000111110100100000000 Sign = 0 Exponent = 11001100 = 204 − 127 = 77 Mantissa = 1.100001111101001 1.100001111101001 × 2 77 Chapter 2 15Section 2-7 Arithmetic Operations with Signed Numbers 31. (a) 33 = 00100001 00100001 15 = 00001111 + 00001111 00110000 (c) 46 = 00101110 11010010 −46 = 11010010 + 00011001 25 = 00011001 11101011 (b) 56 = 00111000 00111000 27 = 00011011 + 11100101 −27 = 11100101 00011101 (d) 110 10 = 01101110 10010010 −110 10 = 10010010 + 10101100 84 = 01010100 100111110 −84 = 10101100 32. (a) 00010110 (b) 01110000 + 00110011 + 10101111 01001001 100011111 33. (a) 10001100 (b) 11011001 + 00111001 + 11100111 11000101 11000000 34. (a) 00110011 00110011 − 00010000 + 11110000 1 00100011 (b) 01100101 01100101 − 11101000 + 00011000 01111101 35. 01101010 01101010 × 11110001 × 00001111 01101010 01101010 100111110 01101010 1011100110 01101010 11000110110 Changing to 2’s complement with sign: 100111001010 36. 0001100101000100 = 00000010 2568 = 2, remainder of 18 Section 2-8 Hexadecimal Numbers 37. (a) 38 16 = 0011 1000 (b) 59 16 = 0101 1001 (c) A14 16 = 1010 0001 0100 (d) 5C8 16 = 0101 1100 1000 (e) 4100 16 = 0100 0001 0000 0000 (f) FB17 16 = 1111 1011 0001 0111 (g) 8A9D 16 = 1000 1010 1001 1101 Chapter 2 16 38. (a) 1110 = E 16 (b) 10 = 2 16 (c) 0001 0111 = 17 16 (d) 1010 0110 = A6 16 (e) 0011 1111 0000 = 3F0 16 (f) 1001 1000 0010 = 982 16 39. (a) 23 16 = 2 × 161 + 3 × 160 = 32 + 3 = 35 (b) 92 16 = 9 × 161 + 2 × 160 = 144 + 2 = 146 (c) 1A 16 = 1 × 161 + 10 × 160 = 16 + 10 = 26 (d) 8D 16 = 8 × 161 + 13 × 160 = 128 + 13 = 141 (e) F3 16 = 15 × 161 + 3 × 160 = 240 + 3 = 243 (f) EB 16 = 14 × 161 + 11 × 160 = 224 + 11 = 235 (g) 5C2 16 = 5 × 162 + 12 × 161 + 2 × 160 = 1280 + 192 + 2 = 1474 (h) 700 16 = 7 × 162 = 1792 40. (a) 168 = 0, remainder = 8 hexadecimal number = 8 16 (c) 1633 = 2, remainder = 1 (LSD) 162 = 0, remainder = 2 hexadecimal number = 21 16 (e) 16284 = 17, remainder = 12 = C 16 (LSD) 1617 = 1, remainder = 1 161 = 0, remainder = 1 hexadecimal number = 11C 16 (g) 164019 = 251, remainder = 3 (LSD) 16251 = 15, remainder = 11 = B 16 1615 = 0, remainder = 15 = F 16 hexadecimal number = FB3 16 (b) 1614 = 0, remainder = 14 = E 16 hexadecimal number = E 16 (d) 1652 = 3, remainder = 4 (LSD) 163 = 0, remainder = 3 hexadecimal number = 34 16 (f) 162890 = 180, remainder = 10 = A 16 (LSD) 16180 = 11, remainder = 4 01611=, remainder = 11 = B 16 hexadecimal number = B4A 16 (h) 166500 = 406, remainder = 4 (LSD) 16406 = 25, remainder = 6 1625 = 1, remainder = 9 161 = 0, remainder = 1 hexadecimal number = 1964 16 41. (a) 37 16 + 29 16 = 60 16 (b) A0 16 + 6B 16 = 10B 16 (c) FF 16 + BB 16 = 1BA 16 Chapter 2 1742. (a) 51 16 − 40 16 = 11 16 (b) C8 16 − 3A 16 = 8E 16 (c) FD 16 − 88 16 = 75 16 Section 2-9 Octal Numbers 43. (a) 12 8 = 1 × 81 + 2 × 80 = 8 + 2 = 10 (b) 27 8 = 2 × 81 + 7 × 80 = 16 + 7 = 23 (c) 56 8 = 5 × 81 + 6 × 80 = 40 + 6 = 46 (d) 64 8 = 6 × 81 + 4 × 80 = 48 + 4 = 52 (e) 103 8 = 1 × 82 + 3 × 80 = 64 + 3 = 67 (f) 557 8 = 5 × 82 + 5 × 81 + 7 × 80 = 320 + 40 + 7 = 367 (g) 163 8 = 1 × 82 + 6 × 81 + 3 × 80 = 64 + 48 + 3 = 115 (h) 1024 8 = 1 × 83 + 2 × 81 + 4 × 80 = 512 + 16 + 4 = 532 (i) 7765 8 = 7 × 83 + 7 × 82 + 6 × 81 + 5 × 80 = 3584 + 448 + 48 + 5 = 4085 44. (a) 815 = 1, remainder = 7 (LSD) 81 = 0, remainder =1 octal number = 17 8 (c) 846 = 5, remainder = 6 (LSD) 85 = 0, remainder = 5 octal number = 56 8 (e) 8100 = 12, remainder = 4 (LSD) 812 = 1, remainder = 4 81 = 0, remainder = 1 octal number = 144 8 (g) 8219 = 27, remainder = 3 (LSD) 827 = 3, remainder = 3 83 = 0, remainder = 3 octal number = 333 8 (b) 827 = 3, remainder = 3 (LSD) 83 = 0, remainder = 3 octal number = 33 8 (d) 870 = 8, remainder = 6 (LSD) 88 = 1, remainder = 0 81 = 0, remainder = 1 octal number = 106 8 (f) 8142 = 17, remainder = 6 (LSD) 817 = 2, remainder = 1 82 = 0, remainder = 2 octal number = 216 8 (h) 8435 = 54, remainder = 3 (LSD) 854 = 6, remainder = 6 86 = 0, remainder = 6 octal number = 663 818 45. (a) 13 8 = 001 011 (b) 57 8 = 101 111 (c) 101 8 = 001 000 001 (d) 321 8 = 011 010 001 (e) 540 8 = 101 100 000 (f) 4653 8 = 100 110 101 011 (g) 13271 8 = 001 011 010 111 001 (h) 45600 8 = 100 101 110 000 000 (i) 100213 8 = 001 000 000 010 001 011 46. (a) 111 = 7 8 (b) 010 = 2 8 (c) 110 111 = 67 8 (d) 101 010 = 52 8 (e) 001 100 = 14 8 (f) 001 011 110 = 136 8 (g) 101 100 011 001 = 5431 8 (h) 010 110 000 011 = 2603 8 (i) 111 111 101 111 000 = 77570 8 Section 2-10 Binary Coded Decimal (BCD) 47. (a) 10 = 0001 0000 (b) 13 = 0001 0011 (c) 18 = 0001 1000 (d) 21 = 0010 0001 (e) 25 = 0010 0101 (f) 36 = 0011 0110 (g) 44 = 0100 0100 (h) 57 = 0101 0111 (i) 69 = 0110 1001 (j) 98 = 1001 1000 (k) 125 = 0001 0010 0101 (l) 156 = 0001 0101 0110 48. (a) 10 = 1010 2 4 bits binary, 8 bits BCD (b) 13 = 1101 2 4 bits binary, 8 bits BCD (c) 18 = 10010 2 5 bits binary, 8 bits BCD (d) 21 = 10101 2 5 bits binary, 8 bits BCD (e) 25 = 11001 2 5 bits binary, 8 bits BCD (f) 36 = 100100 2 6 bits binary, 8 bits BCD (g) 44 = 101100 2 6 bits binary, 8 bits BCD (h) 57 = 111001 2 6 bits binary, 8 bits BCD (i) 69 = 1000101 2 7 bits binary, 8 bits BCD (j) 98 = 1100010 2 7 bits binary, 8 bits BCD (k) 125 = 1111101 2 7 bits binary, 12 ibts BCD (l) 156 = 10011100 2 8 bits binary, 12 bits BCD Chapter 2 1949. (a) 104 = 0001 0000 0100 (b) 128 = 0001 0010 1000 (c) 132 = 0001 0011 0010 (d) 150 = 0001 0101 0000 (e) 186 = 0001 1000 0110 (f) 210 = 0010 0001 0000 (g) 359 = 0011 0101 1001 (h) 547 = 0101 0100 0111 (i) 1051 = 0001 0000 0101 0001 50. (a) 0001 = 1 (b) 0110 = 6 (c) 1001 = 9 (d) 0001 1000 = 18 (e) 0001 1001 = 19 (f) 0011 0010 = 32 (g) 0100 0101 = 45 (h) 1001 1000 = 98 (i) 1000 0111 0000 = 870 51. (a) 1000 0000 = 80 (b) 0010 0011 0111 = 237 (c) 0011 0100 0110 = 346 (d) 0100 0010 0001 = 421 (e) 0111 0101 0100 = 754 (f) 1000 0000 0000 = 800 (g) 1001 0111 1000 = 978 (h) 0001 0110 1000 0011 = 1683 (i) 1001 0000 0001 1000 = 9018 (j) 0110 0110 0110 0111 = 6667 52. (a) 0010 + 0001 0011 (d) 1000 + 0001 1001 (g) 01000000 + 01000111 10000111 (b) 0101 + 0011 1000 (e) 00011000 + 00010001 00101001 (h) 10000101 + 01000111 10000111 (c) 0111 + 0010 1001 (f) 01100100 + 00110011 10010111 Chapter 2 20 53. (a) 000101000110111001101000 ++ (c) 0001011101101000110001001 ++ (e) 010100100110010011000010011100100101 ++ (g) 01 0001100101011001101001011111001011110011000 ++ (b) 000100100110110001010111 ++ (d) 0001011001101000001111001 ++ (f) 01 00010000100110101010010101100001010001 ++ (h) 101001 0001001001011001 110001101000 011100001001 0101011000 ++ invalid invalid invalid invalid invalid invalid invalid invalid Chapter 2 2154. (a) 4 + 3 011100110100 + (c) 6 + 4 000100000110101001000110 ++ (e) 28 + 23 010100010110010010110010001100101000 ++ (g) 113 + 101 00 001000010101 000100000011 0001000100 + (b) 5 + 2 011100100101 + (d) 17 + 12 001010010010001000010111 + (f) 65 + 58 11 000100100001100110101111010101100001100101 ++ (h) 295 + 157 10 01000101000110011000 001111101111 000101010101 0010100101 ++ Section 2-11 Digital Codes 55. The Gray code makes only one bit change at a time when going from one number in the sequence to the next number. Gray for 1111 2 = 1000 Gray for 0000 2 = 0000 56. (a) 1 + 1 + 0 + 1 + 1 Binary (b) 1 + 0 + 0 + 1 + 0 + 1 + 0 Binary 1 0 1 1 0 Gray 1 1 0 1 1 1 1 Gray (c) 1 + 1 + 1 + 1 + 0 + 1 + 1 + 1 + 0 + 1 + 1 + 1 + 0 Binary 1 0 0 0 1 1 0 0 1 1 0 0 1 Gray 57. (a) 1 0 1 0 Gray (b) 0 0 0 1 0 Gray 1 1 0 0 Binary 0 0 0 1 1 Binary (c) 1 1 0 0 0 0 1 0 0 0 1 Gray 1 0 0 0 0 0 1 1 1 1 0 Binary 58. (a) 1 → 00110001 (b) 3 → 00110011 (c) 6 → 00110110 (d) 10 → 0011000100110000 (e) 18 → 0011000100111000 (f) 29 → 0011001000111001 (g) 56 → 0011010100110110 (h) 75 → 0011011100110101 (i) 107 → 001100010011000000110111 Chapter 2 22 59. (a) 0011000 → CAN (b) 1001010 → J (c) 0111101 → = (d) 0100011 → # (e) 0111110 → > (f) 1000010 → B 60. 1001000 1100101 1101100 1101100 1101111 0101110 0100000 H e l l o . # 1001000 1101111 1110111 0100000 1100001 1110010 1100101 H o w # a r e 0100000 1111001 1101111 1110101 0111111 # y o u ? 61. 1001000 1100101 1101100 1101100 1101111 0101110 0100000 48 65 6C 6C 6F 2E 20 1001000 1101111 1110111 0100000 1100001 1110010 1100101 48 6F 77 20 61 72 65 0100000 1111001 1101111 1110101 0111111 20 79 6F 75 3F 62. 30 INPUT A, B 3 0110011 33 16 0 0110000 30 16 SP 0100000 20 16 I 1001001 49 16 N 1001110 4E 16 P 1010000 50 16 U 1010101 55 16 T 1010100 54 16 SP 0100000 20 16 A 1000001 41 16 , 0101100 2C 16 B 1000010 42 16 Section 2-12 Error Codes 63. Code (b) 011101010 has five 1s, so it is in error. 64. Codes (a) 11110110 and (c) 01010101010101010 are in error because they have an even number of 1s. 65. (a) 1 10100100 (b) 0 00001001 (c) 1 11111110 Chapter 2 2366. (a) 1100 1011 0111 (b) 1111 0100 1011 (c) 100011100 10011001 110000101 67. (a) 1100 0111 1011 (b) 1111 1011 0100 (c) 100011100 110000101 010011001 In each case, you get the other number. 68. 101100100000 1010 1001 1010 1100 1010 1100 1010 1100 1010 1100 1010 Remainder = 0110 Append remainder to data . 101100100110 1010 1001 1010 1100 1010 1101 1010 1111 1010 1010 1010 0000 CRC is 101100100110. 69. Error in MSB of transmitted CRC: 001100100110 1010 1001 1010 1100 1010 1101 1010 1110 1010 1000 1010 1011 1010 10 Remainder is 10, indicating an error.