# Combinational Logic Design, computer science homework help

Reminder: Submission must be on time as discussed in class. Where the solution requires a process, show that process, not simply the solution. Your grade in all the homework assignments and exams depends on the legibility of submission: typing or screen shots preferred, ensuring that page arrangement is all the same direction orientation.

1. (2.5 points) Majority rules. Some systems designed, like processing in our brains, require voting inputs to determine output. A majority function produces an output value of 1 if there are more 1’s than 0’s of its inputs. Design a 3-input majority function. Give the simplest possible algebraic function and circuit logic, using only OR and AND gates to implement.

2. (2.5 points) Traffic Light Sequential Design. Traffic light control at a simple ‘+’ intersection uses a binary counter to produce the following sequence of combinations on input lines A, B, C and D: 0000, 0001, 0011, 0010, 0110, 0111, 0101, 0100, 1100, 1101, 1111, 1110, 1010, 1011, 1001, 1000. The sequence continues from the beginning with the next code, 0000. Each combination is applied for 5 seconds, then cycles to the next. These inputs drive combinational logic for six outputs to light lamps as follows:

– Red-north/south (RNS)

– Yellow-north/south (YNS)

– Green-north/south (GNS)

– Red-east/west (REW)

– Yellow- east/west (YEW)

– Green- east/west (GEW)

Each lamp is controlled by its respective output: turned ON for a logic 1 applied and OFF for a 0. Given an entire sequence of 80 seconds, split into 16 five-second intervals, for each direction, its green is on for 30 seconds, yellow for 5 seconds, and red for 45 seconds. (Red intervals overlap 5 seconds for safety.) As the 16 combinations sequence, determine lamps that should be lit in each interval to cause the desired driver behavior. Given starting conditions at beginning of interval 0000 set GNS = 1 and REW = 1 with all other outputs are 0: design the logic to produce the six outputs using AND and OR gates and inverters.

3. (2.5 points) Metering lights. In order to speed up an autobahn, a traffic metering system is under design to release traffic from the entrance ramp onto the highway. Three lanes in parallel approach the metering lights, each with its own stop (red) – go (green) pair of lights. One lane, designated for car pools, is given priority for a green light over the other two lanes, distinguished as left and right. Otherwise, a “round robin” scheme in which the green lights alternate is used (for left and right lanes). Design the control module logic to drive each light (GREEN = 1; RED = 0) given these specifications:

Inputs:

– PS Car pool lane sensor (car present = 1; car absent = 0)

– LS Left lane sensor (car present = 1; car absent = 0)

– RS Right lane sensor (car present = 1; car absent = 0)

– RR Round robin signal (select left = 1; select right = 0)

Outputs:

– PL Car pool lane light (GREEN = 1; RED = 0)

– LL Left lane light (GREEN = 1; RED = 0)

– RL Right lane light (GREEN = 1; RED = 0)

Operation:

1) If there is a car in the car pool lane, PL = 1.

2) If there are no cars in the car pool lane and right lane, but there is a car in the left lane, LL = 1.

3) If there are no cars in the car pool lane and left lane, but there is a car in the right lane, RL = 1.

4) If there are no cars in the car pool lane and cars in both left and right lanes,

i. If RR = 1, then LL = 1.

ii. If RR = 0, then RL = 1.

5) If any PL, LL, or RL is not specified to be 1 above, then it is cleared to value 0.

a) Find the truth table for the control module logic.

b) Find a minimum multiple-level gate implementation with minimum gate-input cost using AND and OR gates and inverters.

4. (2.5 points) Design an 8- Input NAND gate. For each of the following cases, minimize the number of gates used in the multiple-level result:

a) Design an 8- Input NAND gate using 2- Input NAND gates and inverters (NOT gates).

b) Design an 8- Input NAND gate using 2- Input NAND gates,2 – Input NOR gates, and inverters (NOT gates) only if needed.

c) Compare the number of gates used in a) and b).