Logic Ckts 1 Quiz 3 New Set A B C And D(1)

LOGIC CIRCUITS & SWITCHING THEORY I Professor: Engr. Rafael G. Maramba

Quiz No.3 SET A Problem 1

50 pts.

DESIGN A 4-INPUT PRIORITY ENCODER WITH INPUTS AND OUTPUTS AS SHOWN IN THE TABLE BELOW. THE TRUTH TABLE REPRESENTS THE CASE IN WHICH D 0 HAS THE HIGHEST PRIORITY AND D3 HAVING THE LOWEST PRIORITY. The valid bit V is equal to 1 only if there is a valid input condition. SHOW THE FOLLOWING: (a) The truth table for the required encoder as shown below (b) The map with the most economical grouping of minterms in determining the output signals including the valid bit V. (c) The BOOLEAN EXPRESSION FOR EACH OUTPUT SIGNAL A1, A2, & V (in SOP form). ENCIRCLE YOUR FINAL ANSWER.

INPUT SIGNAL D3 NOTES:

Problem 2

D2

D1

OUTPUT SIGNAL D0

minterm designation

A1

A0

V

When D0 (button 0) is pressed, the output signal is 0. When D3 (button 3) is pressed, the output signal is 3. Show all possible input combinations in ascending order.

60 pts.

CONSTRUCT A COMBINATIONAL CIRCUIT THAT ACCEPTS A 2-BIT BINARY NUMBER (XY) AND GENERATES A 4-BIT BINARY NUMBER OUTPUT (ABCD) EQUAL TO THE SQUARE OF THE INPUT NUMBER. SHOW CLEARLY THE FOLLOWING: (a) TRUTH TABLE OF THE CIRCUIT (b) MAPS WITH THE MOST ECONOMICAL GROUPING OF MINTERMS (c) THE EXPRESSION FOR EACH OUTPUT SIGNAL IN SOP FORM (d) THE LOGIC DIAGRAM

Problem 3

40 pts.

CONSTRUCT A 3-TO-8 LINE DECODER WITH AN ENABLE INPUT e USING 2-TO-4 LINE DECODERS WITH ENABLE INPUT AS ITS BASIC BUILDING BLOCK. SHOW CLEARLY THE FOLLOWING:. (a) THE CIRCUIT IN BLOCK DIAGRAM FORM (CLEARLY LABEL EVERYTHING) NOTE: For input signal variables, use A, B, C, etc… For output signal variables, use Z0, Z1, Z2, Z3, ETC… (b) TRUTH TABLE FOR THE CIRCUIT CONCERNED. NOTE: The truth table must conform with the operation of your circuit in Problem 1(a). “ Only he that has traveled the road knows where the holes are deep.” - Chinese Proverb

LOGIC CIRCUITS & SWITCHING THEORY I Professor: Engr. Rafael G. Maramba

Quiz No.3 SET B Problem 1

60 pts.

CONSTRUCT THE CIRCUIT DIAGRAM OF A 4-TO-16 LINE DECODER WITH AN ENABLE INPUT USING A MINIMUM NUMBER OF 2-TO-4 LINE DECODERS WITH ENABLE INPUT AS ITS BASIC BUILDING BLOCK. SHOW THE FOLLOWING: (a) THE CIRCUIT IN BLOCK DIAGRAM FORM (CLEARLY LABEL EVERYTHING) NOTE: For input signal variables, use A, B, C, etc… For output signal variables, use Z0, Z1, Z2, Z3, ETC… (b) TRUTH TABLE FOR THE CIRCUIT CONCERNED. NOTE:

Problem 2

The truth table must conform with the operation of your circuit in Problem 1(a).

50 pts.

DESIGN AN EXCESS-3-to-BCD CODE CONVERTER, REQUIRING THAT ALL INVALID INPUT COMBINATIONS GIVE 0000 AS THE OUTPUT CODE. SHOW CLEARLY THE FOLLOWING: (a) TRUTH TABLE (input entries must be in ascending order) (b) MAPS WITH MOST ECONOMICAL GROUPING OF MINTERMS (c) THE BOOLEAN EXPRESSION FOR THE OUTPUT SIGNALS IN SOP FORM. ENCIRCLE FINAL ANSWER. A

Excess-3 Code B C

Problem 3

D

Minterm (m)

W

BCD Code X Y

Z

40 pts.

DESIGN A COMBINATIONAL CIRCUIT THAT CAN DETECT AN ERROR IN THE REPRESENTATION OF A DECIMAL DIGIT IN BCD. IN OTHER WORDS, THE CIRCUIT’S OUTPUT IS EQUAL TO 1 WHEN THE INPUT ABCD CONTAINS ANY ONE OF THE SIX UNUSED BIT COMBINATIONS IN THE BCD CODE. SHOW CLEARLY THE FOLLOWING: (a) THE CIRCUIT’S TRUTH TABLE (b) MAP with MOST ECONOMICAL GROUPING OF MINTERMS (c) THE EXPRESSION OF THE OUTPUT SIGNAL F(A,B,C,D) IN SOP FORM. (d) THE LOGIC DIAGRAM NOTE: Encircle FINAL ANSWER.

“ Only he that has traveled the road knows where the holes are deep.” - Chinese Proverb

LOGIC CIRCUITS & SWITCHING THEORY I Professor: Engr. Rafael G. Maramba

Quiz No.3 SET C Problem 1.

50 pts.

DESIGN A COMBINATIONAL CIRCUIT WITH THREE INPUTS (XYZ) AND ONE OUTPUT (F). THE OUTPUT SIGNAL IS 1 WHEN THE BINARY VALUE OF THE INPUTS IS AN ODD NUMBER. SHOW CLEARLY THE FOLLOWING: (a) TRUTH TABLE OF THE ABOVE CIRCUIT (b) MAP with the most economical GROUPING OF MINTERMS (c) the BOOLEAN EXPRESSION OF THE OUTPUT SIGNAL in SOP form . ENCIRCLE FINAL ANSWERS.

Problem 2

60 pts.

CONSTRUCT A COMBINATIONAL CIRCUIT THAT ACCEPTS A 2-BIT BINARY NUMBER (XY) AND GENERATES A 4-BIT BINARY NUMBER OUTPUT (ABCD) EQUAL TO THE SQUARE OF THE INPUT NUMBER. SHOW CLEARLY THE FOLLOWING: (b) TRUTH TABLE OF THE CIRCUIT (e) MAPS WITH THE MOST ECONOMICAL GROUPING OF MINTERMS (f) THE EXPRESSION FOR EACH OUTPUT SIGNAL IN SOP FORM (g) THE LOGIC DIAGRAM

Problem 3

40 pts.

DESIGN A COMBINATIONAL CIRCUIT THAT CAN DETECT AN ERROR IN THE REPRESENTATION OF A DECIMAL DIGIT IN BCD. IN OTHER WORDS, THE CIRCUIT’S OUTPUT IS EQUAL TO 1 WHEN THE INPUT ABCD CONTAINS ANY ONE OF THE SIX UNUSED BIT COMBINATIONS IN THE BCD CODE. SHOW CLEARLY THE FOLLOWING: (e) THE CIRCUIT’S TRUTH TABLE (f) MAP with MOST ECONOMICAL GROUPING OF MINTERMS (g) THE EXPRESSION OF THE OUTPUT SIGNAL F(A,B,C,D) IN SOP FORM. (h) THE LOGIC DIAGRAM NOTE: Encircle FINAL ANSWER.

“ Only he that has traveled the road knows where the holes are deep.” - Chinese Proverb