Second Year – CIS Course Teacher: Maria Waqas CS-214 DIGITAL LOGIC DESIGN PRACTICE PROBLEMS

Second Year – CIS Course Teacher: Maria Waqas

CS-214 DIGITAL LOGIC DESIGN PRACTICE PROBLEMS 1. Five soldiers A, B, C, D and E volunteer to perform an important military task if their following conditions

are satisfied: i. Either A or B or both must go. ii. Either C or E but not both must go. iii. Either both A and C go or neither goes. iv. If B goes, then A and C must also go. Suggest a single gate implementation for each of the above conditions (one gate for each condition). 2. Design a combinational circuit that receives a 4-bit value at its input and produces an output z. the output z of the circuit is to be 1 if and only if the inputs represent a number that is either 0 or a power of 2. Derive the simplified expression for output z and draw logic diagram. 3. Design a combinational circuit that receives a 4-bit value at its input and produces an output z. the output z of the circuit is to be 1 if and only if the inputs represent a number that is completely divisible by 3 or 7. Derive the simplified expression for output z and draw logic diagram. 4. Design a combinational circuit that receives a 4-bit value at its input and produces an output z. the output z of the circuit is to be 1 if and only if the inputs represent a number that is completely divisible by 3 and 6. Derive the simplified expression for output z and draw logic diagram. 5. A logic circuit has four inputs. The output z is to be 1 when a majority of the inputs are 0. Find the simplified logic expression for z using k-map. 6. A logic circuit is to be designed having 4 inputs y1, y0 , x1 and x0. The pairs of bits y1y0 and x1x0 represent 2-bit binary numbers with y1 and x1 as the most significant bits. The only circuit output z is to be 1 if and only if the binary number x1x0 is greater than or equal to the binary number y1y0. Find the simplified logic expression and draw logic diagram. 7. The specifications for a submarine state that a SURFACE command shall be initiated automatically under certain conditions related to oxygen level (X), battery charge (B), and fresh water supply (W). Each of these variables becomes 0 if the quantity it represents is dangerously low. The SURFACE command shall be initiated if:  Battery charge and oxygen level are both low; or  Fresh water is low, battery charge is high, and oxygen is low; or  Fresh water is high and oxygen level is low. Find the simplest possible logic circuit that can control the SURFACE. 8. A water-well pump is to be turned on automatically if the water level is low in any two or more of the three reservoirs it supplies. Water-level detectors in the reservoirs each generate a logic 1 if the level in the reservoir is low. Design a logic system that turns on the pump by generating a logical 0 in response to inputs received from the level detectors. Use boolean theorems for solution. 9. On the intersection of a main highway with the secondary access road, vehicle detection sensors are placed along lanes C & D (main road) and A & B (access road). These sensor outputs are LOW(0) when no vehicle is present and HIGH(1) when a vehicle is present. The intersection traffic is to be controlled by two traffic lights, N-S and E-W, using the following logic:  The E-W (east-west) traffic will be green whenever both lanes C and D are occupied.  The E-W light will be green whenever either C or D is occupied but lanes A and B are both not occupied.

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The N-S (north-south) light will be green whenever both lanes A and B are occupied but C and D are both not occupied.  The N-S light will also be green when either A or B is occupied while C and D are both vacant.  The E-W light will be green when no vehicle is present. Using the sensor outputs A, B, C and D as inputs, design a logic circuit to control the traffic lights. There should be two outputs N-S and E-W, which go HIGH(1) when the corresponding light is to be green. Simplify the circuit as much as possible.

10. An air-conditioning unit is controlled by four variables: Temperature T, humidity H, the time of the day D, and the day of the week W. The unit is turned on under any of the following circumstances: i. The temperature exceeds 78o F, and the time of the day is between 8 a.m. and 5 p.m. ii. The humidity exceeds 85%, the temperature exceeds 78o F, and the time of the day is between 8 a.m. and 5 p.m. iii. The humidity exceeds 85%, the temperature exceeds 78o F, and it is a weekend. iv. It is Saturday or Sunday and humidity exceeds 85%. Write a logic expression for controlling the air-conditioning unit. Simplify the expression obtained as far as possible. 11. Jones, Smith and Brown are prosecution witnesses at Willson’s trial. Each of the witnesses is given a lie detector test. The jury is willing to convict Wilson if Jones and Smith both pass the lie detector test. The jury is also willing to convict if either Jones or Smith (or both) fail the test but Brown passes it. Find the simplest way (using Boolean theorems) to express the terms under which Wilson will be convicted. 12. The inputs to a certain computer circuit are the 4 bits A3, A2, A1 and A0 of a binary number, where A3 is the most significant bit. The circuit is required to produce a 1 if and only if all the following conditions hold:  The most significant bit is 1 or any of the other bits are 0;  A2 is 1 or any of the other bits are 0;  Any of the four bits are zero. Use K- map to find the simplest logic expression for the circuit. Also draw the logic diagram. 13. Design a combinational circuit with three inputs, x, y and z, and three outputs, A, B and C. When the binary input is 0, 1, 2 or 3, the binary output is one greater than the input. When the binary input is 4, 5, 6 or 7, the binary output is one less than the input. 14. Design a combinational circuit whose input is a 4-bit number and output is the 2’s complement of the input number. 15. Five people judge a certain competition. The vote of each is indicated by 1 (pass) or 0 (fail) on a signal line. The five signal lines form the input to a logic circuit. The rules of the competition allow only one dissenting vote. If the vote is 2-3 or 3-2, the competition must continue. The logic circuit is to have two outputs, x and y. if the vote is 4-1 or 5-0 to pass, xy = 11. If the vote is 4-1 or 5-0 to fail, xy = 00. If the vote is 3-2 or 2-3, xy = 10. Design the required circuit. 16. A, B, C and D are members of the board of trustees of an investment company. Decisions are made by the following criterions. A BUY order is placed if:  A, B and D vote no and C votes yes,  Or A and C vote no and rest vote yes,  Or B and C vote yes and rest vote no,  Or B votes yes and others vote no,  And it is impossible for C and D to vote yes simultaneously. Answer the following questions: a. Design a simplified logic circuit (equation + diagram) that will make the buy decision for these confused stock brokers. b. Is there more than one solution to this problem? If yes, write expression for all possible solutions.

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17. A lawn sprinkling system at a large estate is to be automatically controlled by certain combinations of the following variables: Season ( S = 1 if summer, 0 otherwise ) Moisture content of soil ( M = 1 if high, 0 if low ) Outside temperature ( T = 1 if high, 0 if low ) Outside humidity ( H = 1 if high, 0 if low ) The landscape architect designing the system wants the sprinkler to be turned ON under any of the following circumstances: i. Moisture content is low in the winter; or ii. Temperature is high and moisture content is low in the summer; or iii. Temperature is high and humidity is high in the summer; iv. It is impossible that temperature is low in the summer. Use a Karnaugh map to find the simplest possible logic expression for turning ON the sprinkler system. 18. There are four switches (S1, S2, S3 and S4) that are part of the control circuitry in a copying machine. The switches are at various points along the path of the copy paper as the paper passes through the machine. Each switch is normally open (logic 0), and as the paper passes over the switch, the switch closes (logic 1). It is impossible for the switches S1 and S4 to be closed at the same time. Design simplified logic circuit to produce a HIGH output whenever three or more switches are closed at the same time. 19. In a digital system, all decimal digits and the four operators (+ , − , × , ÷) are coded in the forms of unique combinations of binary bits. The codes are assigned as follows: Digit / operator Code (in decimal) Digit / operator Code (in decimal) + 0 ÷ 7 0 1 4 8 − 2 5 9 1 3 6 10 2 4 7 11 3 5 8 12 × 6 9 13 i. ii.

What is the minimum number of bits required to represent the coded input in this system? Design a combinational circuit using k-map that receives the coded input and produces an output 0 if it is a decimal digit and 1 if it is an operator.

20. A digital computer has five output devices connected to it as follows: Mode description Code Mode description Code Punched card 001 Punched tape, numeric 100 Magnetic tape 010 Punched tape, alphabetic 101 Type writer 011 The selection of an output device is controlled by signals on three parallel lines, denoted x, y and z, according to the codes indicated above. Design a combinational circuit that gives 1 at its output whenever punched tape is selected.

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