4-7. Design a combinational circuit that multiplies by 5 an input decimal digit represented in BCD. The output is also in BCD. Show that the outputs can be obtained from the input lines without using any logic gates.

Database System Concepts
7th Edition
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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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exciusive-OR gates.
REFERENCES
1.
Rhyne, V. T., Fundamentals of Digital Systems Design. Englewood Cliffs, N.J.: Prentice-Hall. Inc.,
1973.
2.
Peatman, J. P., The Design of Digital Systems. New York: MeGraw-Hill Book Co., 1972.
3. Nagle, H. T. Jr., B. D. Carrol, and J. D. Irwin, An Introduction to Computer Logic. Englewood Cliffs,
N. J.: Prentice-Hall. Inc., 1975.
4. Hill, F. J., and G. R. Peterson, Introduction to Switching Theory and Logical Design, 2nd. ed. New
York: John Wiley & Sons. Inc. 1974.
5.
J.: Prentice-Hall. Inc., 1963.
Maiey, G. A., and J. Earle, The Logic Design of Transistor Digital Computers. Englewood Cliffs, N.
6. Friedman, A. D., and P. R. Menon, Theory and Design of Switching Circuits. Woodland Hills, Calif.:
Computer Science Press. Inc., 1975.
PROBLEMS
4-1
A combinational circuit has four inputs and one output. The output is equal to 1 when (1) all the
inputs are equal to 1 or (2) none of the inputs are equal to 1 or (3) an odd number of inputs are equal
to I.
(a) Obtain the truth table.
(b) Find the simplified output function in sum of products.
(c) Find the simplified output function in product of sums.
(d) Draw the two logic diagrams.
4-2.
Design a combinational circuit that accepts a three-bit number and generates an output binary num-
ber equal to the square of the input number.
It is necessary to multiply two binary numbers, each two bits long, in order to form their product in
binary. Let the two numbers be represented by a,, a, and b, b, where subscript 0 denotes the least
significant bit.
(a) Determine the number of output lines required.
4-3.
(b) Find the simplified Boolean expressions for each output.
4-4. Repeat problem 4-3 to form the sum (instead of the product) of the two binary numbers.
4-5. Design a combinational circuit with four input lines that represent a decimal digit in BCD and four
output lines that generate the 9's complement of the input digit.
4-6. Design a combinational circuit whose input is a four-bit number and whose output is the 2's comple-
ment of the input number.
4-7.
Design a combinational circuit that multiplies by 5 an input decimal digit represented in BCD. The
output is also in BCD. Show that the outputs can be obtained from the input lines without using any
logic gates.
4.8
Design a combinational circuit that detects an error in the representation of a decimal digit in BCD.
In other words, obtain a logic diagram whose output is logic-1 when the inputs contain an unused
combination in the code.
134 Chapter 4
4-9. Implement a full-subtractor with two half-subtractors and an OR gate.
4-10. A BCD-to-seven-segment decoder is a combinational circuit that accepts a decimal digit in BCD
and generates the
playing the decimal digit. The seven outputs of the decoder (a, b, c, d, ef, g) select the corresponding
segments in the display as shown in Fig. P4-14(a). The numeric designation chosen to repre-
sent the decimal digit is shown in Fig. P4-14(b). Design the BCD-to-seven-segment decoder
appropriate outputs for selection of segments in a display indicator used for dis-
circuit.
a
E2345678
f
(a) Segment designation
(b) Numerical designation for display
Figure P4.14
A
-F2
B
-F,
Figure P4.15
4-11. Analyze the two-output combinational circuits shown in Fig. P4-15. Obtain the Boolean functions
for the two outputs and explain the circuit operation.
4-12. Derive the truth table of the circuit shown in Fig, P4-15.
Transcribed Image Text:exciusive-OR gates. REFERENCES 1. Rhyne, V. T., Fundamentals of Digital Systems Design. Englewood Cliffs, N.J.: Prentice-Hall. Inc., 1973. 2. Peatman, J. P., The Design of Digital Systems. New York: MeGraw-Hill Book Co., 1972. 3. Nagle, H. T. Jr., B. D. Carrol, and J. D. Irwin, An Introduction to Computer Logic. Englewood Cliffs, N. J.: Prentice-Hall. Inc., 1975. 4. Hill, F. J., and G. R. Peterson, Introduction to Switching Theory and Logical Design, 2nd. ed. New York: John Wiley & Sons. Inc. 1974. 5. J.: Prentice-Hall. Inc., 1963. Maiey, G. A., and J. Earle, The Logic Design of Transistor Digital Computers. Englewood Cliffs, N. 6. Friedman, A. D., and P. R. Menon, Theory and Design of Switching Circuits. Woodland Hills, Calif.: Computer Science Press. Inc., 1975. PROBLEMS 4-1 A combinational circuit has four inputs and one output. The output is equal to 1 when (1) all the inputs are equal to 1 or (2) none of the inputs are equal to 1 or (3) an odd number of inputs are equal to I. (a) Obtain the truth table. (b) Find the simplified output function in sum of products. (c) Find the simplified output function in product of sums. (d) Draw the two logic diagrams. 4-2. Design a combinational circuit that accepts a three-bit number and generates an output binary num- ber equal to the square of the input number. It is necessary to multiply two binary numbers, each two bits long, in order to form their product in binary. Let the two numbers be represented by a,, a, and b, b, where subscript 0 denotes the least significant bit. (a) Determine the number of output lines required. 4-3. (b) Find the simplified Boolean expressions for each output. 4-4. Repeat problem 4-3 to form the sum (instead of the product) of the two binary numbers. 4-5. Design a combinational circuit with four input lines that represent a decimal digit in BCD and four output lines that generate the 9's complement of the input digit. 4-6. Design a combinational circuit whose input is a four-bit number and whose output is the 2's comple- ment of the input number. 4-7. Design a combinational circuit that multiplies by 5 an input decimal digit represented in BCD. The output is also in BCD. Show that the outputs can be obtained from the input lines without using any logic gates. 4.8 Design a combinational circuit that detects an error in the representation of a decimal digit in BCD. In other words, obtain a logic diagram whose output is logic-1 when the inputs contain an unused combination in the code. 134 Chapter 4 4-9. Implement a full-subtractor with two half-subtractors and an OR gate. 4-10. A BCD-to-seven-segment decoder is a combinational circuit that accepts a decimal digit in BCD and generates the playing the decimal digit. The seven outputs of the decoder (a, b, c, d, ef, g) select the corresponding segments in the display as shown in Fig. P4-14(a). The numeric designation chosen to repre- sent the decimal digit is shown in Fig. P4-14(b). Design the BCD-to-seven-segment decoder appropriate outputs for selection of segments in a display indicator used for dis- circuit. a E2345678 f (a) Segment designation (b) Numerical designation for display Figure P4.14 A -F2 B -F, Figure P4.15 4-11. Analyze the two-output combinational circuits shown in Fig. P4-15. Obtain the Boolean functions for the two outputs and explain the circuit operation. 4-12. Derive the truth table of the circuit shown in Fig, P4-15.
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