Assignment Instruction

This is an individual assignment which you must complete and submit. There are 3 questions in total of which you must answer all and the results will contribute 20% of your coursework mark. All assignment submissions must be handwritten (in legible handwriting) and include the cover page found on the last page of this assignment sheet. No binding or plastic cover is necessary (just staple)

Question 1

A paper tape reader used as an input device to a machine has four rows  of holes as shown.  A hole punched in the tape indicates a logic 1, and no hole indicates a logic 0. As each hole pattern passes under the photocells, the pattern is translated into logic signals on lines A, B, C, and D.

All patterns of holes indicate a valid character with two exceptions. A pattern consisting of none of the possible holes punched is not used because it is impossible to distinguish between this pattern and the unpunched space between patterns. An incorrect pattern punched on the tape is erased by punching all four holes in that position. Therefore, a valid character punched on the tape will have at least one hole but will not have all four holes punched.

Design a combinational logic circuit that read valid characters, which has the output 1. Perform the below steps.

(i) Derive the truth table for the above problem.  

 (ii) Minimized the expression into simplified SOP form using K-map.

(iii)Draw the combinational logic diagram based on the simplified Boolean expression as in (ii). 
Question 2

Assume that in a cockpit system, four sensors of S1, S2, S3, and S4 are placed at different places in an aircraft to detect the small leaks in pipelines. If two or more sensors are activated, an alarm system output will be enabled. Input signal lines indicate the sensors (if activated-1, if not activated-0).  

(i) Draw the truth table for the above problem indicating all possible combinations for the sensors and the corresponding status of the alarm system output. 
(ii) Minimize the expression into simplified POS form (you may choose k-map or Boolean algebra). 
(iii) Draw the combinational logic diagram based on the simplified Boolean expression as (ii). 

Question 3

Design a magnitude comparator that takes two 2-bit binary numbers, A2A, and determine their status based on below condition,

If two numbers are equal then EQUAL =1

If A2A 1 greater than B2B then GREATER = 1

If A2A 1

less than B2B 11 then LESS = 1

This comparator circuit contains of FOUR inputs (A2A 1 and B2B) and THREE outputs

(EQUAL, GREATER and LESS). 

(i) Derive the truth table for the above problem.  1

(ii) Minimized the expression into simplified SOP form using K-map.

(iii)Draw the combinational logic diagram based on the simplified Boolean expression as in (ii). 
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