Good evening, im having trouble with an exercise for my circuit design class, can you help?

 

 

Module 3 Exercises
CESC 220 Digital Circuit Design
1. A flow rate sensing device used on a liquid transport pipeline functions as follows. The
device provides a 5-bit output where all five bits are zero if the flow rate is less than 10
gallons per minute. The first bit is 1 if the flow rate is at least 10 gallons per minute; the
first and second bits are 1 if the flow rate is at least 20 gallons per minute; the first,
second, and third bits are 1 if the flow rate is at least 30 gallons per minute; and so on.
The five bits, represented by the logical variables A, B, C, D, and E, are used as inputs to
a device that provides two outputs Y and Z.
a) Write an equation for the output Y if we want Y to be 1 iff the flow rate is less than
30 gallons per minute.
b) Write an equation for the output Z if we want Z to be 1 iff the flow rate is at least
20 gallons per minute but less than 50 gallons per minute.
2. (a) Implement a full subtracter using a minimum number of gates.
(b) Compare the logic equations for the full adder and full subtracter. What is the relation
between si and di? Between ci+1 and bi+1?
Attach Word or PDF documents as necessary to include any truth tables and/or equations
with symbols.
3. Design a circuit which will perform the following function on three 4-bit numbers:
(X3X2X1 X0 + Y3Y2Y1Y0) – Z3Z2Z1Z0
It will give a result S3S2S1S0, a carry, and a barrow. Use eight full adders and any other
type of gates. Assume that negative numbers are represented in 2’s complement.
Attach a Word or PDF document, or image file of your circuit.
4. A bank vault has three locks with a different key for each lock. Each key is owned by a
different person. To open the door, at least two people must insert their keys into the
assigned locks. The signal lines A, B, and C are 1 if there is a key inserted into the lock 1,
2, or 3, respectively. Write an equation for the variable Z which is 1 iff the door should
open.

Attachments:

• 1493282985-CESC_220_M03_Exercise.docx