Digital-Systems-HW5

pdf

School

Arizona State University *

*We aren’t endorsed by this school

Course

MISC

Subject

Electrical Engineering

Date

Feb 20, 2024

Type

pdf

Pages

Uploaded by EarlCrown13337

Digital Systems HW 5 Karnaugh Maps 1. Write the minimal expression corresponding to the following map. Indifferent variables are represented by the letter 'd' (don't care). w’y’+w’x+y’z+xyz’+wx’z 2. Given the following function: F(a,b,c,d) = Σ(1,2,3,11,12,13,14,15)+ d(5,7,9) a) Make a Karnaugh Map. a’b’ a’b ab ab’ c’d’ 0 0 1 0 c’d 1 0 1 0 cd 1 0 1 1 cd’ 1 0 1 0 b) ab + acd + a’b’d + a’b’c 3. Reduce the following expressions to SOP and POS forms using Karnaugh maps: a) x'+xyz'+(x+x'y'z)(x(x'+y'+z)') x’y’ x’y xy xy’ z’ 1 1 1 0 z 1 1 0 0 SOP: x’+yz’ POS: (x’+z’)(x’+y) b) (x+xy)(x+x'z)(y'+yz')+(x(y'+z'))' x’y’ x’y xy xy’ z’ 1 1 1 1 z 1 1 0 1 SOP: x’+y’+z’ POS: x’+y’+z’

4. Reduce the following function to SOP and POS forms using Karnaugh maps: F(a,b,c,d,e) = π(4,6,7,9,11,12,13,14,15,20,22,25,27,28,30) · π Φ (1,5,29,31) a’ b’c’ b’c bc bc’ a b’c’ b’c bc bc’ d’e’ 1 0 0 1 d’e’ 1 0 0 1 d’e Φ Φ 0 0 d’e 1 1 Φ 0 de 1 0 0 0 de 1 1 Φ 0 de’ 1 0 0 1 de’ 1 0 0 1 SOP: b’c’ + e’c’ + ab’e a b+c b+c’ b’+c’ b’+c a’ b+c b+c’ b’+c’ b’+c d+e 1 0 0 1 d+e 1 0 0 1 d+e’ Φ Φ 0 0 d+e’ 1 1 Φ 0 d’+e’ 1 0 0 0 d’+e’ 1 1 Φ 0 d’+e 1 0 0 1 d’+e 1 0 0 1 POS: ( a+c’ )( c’+e )( b’+e’ )

Quine-Mcclusky Tables 1. Reduce the following function to SOP and POS forms using the Quine- Mcclusky method: F abcde = Π(6, 7, 14, 15, 17, 19, 21, 23, 25, 29)·Π Φ (1, 5, 9, 13, 18, 22, 30) = Σ(0,2,3,4,8,10,11,12,16,20,24,26,27,28,31)+Σ Φ (1,5,9,13,18,22,30) 0 00000 0,1 0000- 0,1,2,3 000-- 0,1,2,3,8,9,10,11 0-0-- 1 00001 0,2 000-0 0,1,4,5 00-0- 0,1,4,5,8,9,12,13 0--0- 2 00010 0,4 00-00 0,1,8,9 0-00- 0,2,8,10,16,18,24,26 --0-0 4 00100 0,8 0-000 0,2,8,10 0-0-0 0,4,8,12,16,20,24,28 ---00 8 01000 0,16 -0000 0,2,16,18 -00-0 16,18,20,22,24,26,28,30 1---0 16 10000 1,3 000-1 0,4,8,12 0--00 3 00011 1,5 00-01 0,4,16,20 -0-00 5 00101 1,9 0-001 0,8,16,24 --000 9 01001 2,3 0001- 1,3,9,11 0-0-1 10 01010 2,10 0-010 1,5,9,13 0--01 12 01100 2,18 -0010 2,3,10,11 0-01- 18 10010 4,5 0010- 2,10,18,26 --010 20 10100 4,12 0-100 4,5,12,13 0-10- 24 11000 4,20 -0100 4,12,20,28 --100 11 01011 8,9 0100- 8,9,10,11 010-- 13 01101 8,10 010-0 8,9,12,13 01-0- 22 10110 8,12 01-00 8,10,24,26 -10-0 26 11010 8,24 -1000 8,12,24,28 -1-00 28 11100 16,18 100-0 16,18,20,22 10--0 27 11011 16,20 10-00 16,18,24,26 1-0-0 30 11110 16,24 1-000 16,20,24,28 1--00 31 11111 3,11 0-011 10,11,26,27 -101- 5,13 0-101 18,22,26,30 1--10 9,11 010-1 20,22,28,30 1-1-0 9,13 01-01 24,26,28,30 11--0 10,11 0101- 26,27,30,31 11-1- 10,26 -1010 12,13 0110- 12,28 -1100 18,22 10-10 18,26 1-010 20,22 101-0 20,28 1-100 24,26 110-0

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version

Access to all documents
Unlimited textbook solutions
24/7 expert homework help

24,28 11-00 11,27 -1011 22,30 1-110 26,27 1101- 26,30 11-10 28,30 111-0 27,31 11-11 30,31 1111- 0 2 3 4 8 10 11 12 16 20 24 26 27 28 31 10,11,26,27 x x x x 26,27,30,31 x x x 0,1,2,3,8,9,10,11 x x x x x x 0,1,4,5,8,9,12,13 x x x x 0,2,8,10,16,18,24,26 x x x x x x x 0,4,8,12,16,20,24,28 x x x x x x x x 16,18,20,22,24,26,28,30 x x x x x SOP: F = abd + a’c’ + d’e’ group d Group d Group d 1 00001 1,5 4 1,5,9,13 4,8 1,5,9,13,17,21,25,29 4,8,16 5 00101 1,9 8 1,5,17,21 4,16 6 01010 1,17 16 1,9,17,25 8,16 9 01001 5,7 2 5,7,13,15 2,8 17 10001 5,13 8 5,7,21,23 2,16 18 10010 5,21 16 5,13,21,29 8,16 7 00111 6,7 1 6,7,14,15 1,8 13 01101 6,14 8 6,7,22,23 1,16 14 01110 6,22 16 6,14,22,30 8,16 19 10011 9,13 4 9,13,25,29 4,16 21 10101 9,25 16 17,19,21,23 2,4 22 10110 17,19 2 17,21,25,29 4,8 25 11001 17,21 4 18,19,22,23 1,4 15 01111 17,25 8 23 10111 18,19 1 29 11101 18,22 4 30 11110 7,15 8 7,23 16

13,15 2 13,29 16 14,15 1 14,30 16 19,23 4 21,23 2 21,29 8 22,23 1 22,30 8 25,29 4 6 7 14 15 17 19 21 23 25 29 5,7,13,15 x x 5,7,21,23 x x x 0-01- 6,7,14,15 x x x x 6,7,22,23 x x 6,14,22,30 x x 10--0 17,19,21,23 x x x x 18,19,22,23 x x ---01 1,5,9,13,17,21,25,29 x x x x POS: (a+c+d’)(a’+b+e)(d+e’) 2. Given the function: f(W,X,Y,Z) = Σ(0,1,3,5,8,10,11,12) + Σ Φ (9,14) a) What are the prime implicants of the function? Group d Group d 0 0000 0,1 1 0,1,8,9 1,8 1 0001 0,8 8 1,3,9,11 2,8 8 1000 1,3 2 8,9,10,11 1,2 3 0011 1,5 4 8,10,12,14 2,4 5 0101 1,9 8 9 1001 8,9 1 10 1010 8,10 2 12 1100 8,12 4 11 1011 3,11 8 14 1110 9,11 2 10,11 1 10,14 4 12,14 2

PIs are (0,1,8,9), (1,3,9,11), (8,9,10,11), (8,10,12,14) and (1,5) b) What are the Essential Prime Implicants (EPI) of the function? EPIs are (0,1,8,9), (1,3,9,11), (8,10,12,14) and (1,5) c) What is the minimal expression in SOP form? x’y’+x’z+wz’+w’y’z

Your preview ends here

Eager to read complete document? Join bartleby learn and gain access to the full version