Shakel Chowdhury
Reputation: 11
How can I find the equation from this truth-table using k-map or QM method?
How can I find the equation from this truth table using k-map or QM method?
Upvotes: 1
Views: 240
Answers (1)
user11844224
Reputation:
The answer is that the question is flawed. The code below finds these flaws/"CONFLICTS":
Mac_3.2.57$cat kmap_so_60848669--how-can-i-find-the-equation-from-this-truth-table-using-k-map-or-qm-method.c
#include <stdio.h>
#define F0 0
#define F1 1
#define F2 2
#define F3 3
#define ALUOp0 4
#define ALUOp1 5
#define Operation2 6
#define Operation1 7
#define Operation0 8
#define dontKnow 2
#define dontCare 3
int main(void){
int op[64][9];
/* populate inputs */
for(int i=0; i<64; i++){
if(i % 2 == 1){
op[i][0] = 1;
}else{
op[i][0] = 0;
}
if(i/2 % 2 == 1){
op[i][1] = 1;
}else{
op[i][1] = 0;
}
if(i/4 % 2 == 1){
op[i][2] = 1;
}else{
op[i][2] = 0;
}
if(i/8 % 2 == 1){
op[i][3] = 1;
}else{
op[i][3] = 0;
}
if(i/16 % 2 == 1){
op[i][4] = 1;
}else{
op[i][4] = 0;
}
if(i/32 % 2 == 1){
op[i][5] = 1;
}else{
op[i][5] = 0;
}
op[i][Operation2] = 3;
op[i][Operation1] = 3;
op[i][Operation0] = 3;
}
/* populate outputs based on CKT */
for(int i=0; i<64; i++){
/* from given ckt */
op[i][Operation2] = op[i][ALUOp0] || (op[i][ALUOp1] && op[i][F1]);
op[i][Operation1] = !op[i][ALUOp1] || !op[i][F2];
op[i][Operation0] = op[i][ALUOp1] && (op[i][F3] || op[i][F0]);
}
/* print truth table */
printf( "ALUOp1 ALUOp0 F3 F2 F1 F0 Operation210 Notes\n");
for(int i=0; i<64; i++){
printf("%d %d %d %d %d %d %d%d%d ", op[i][ALUOp1], op[i][ALUOp0], op[i][F3], op[i][F2], op[i][F1], op[i][F0], op[i][Operation2], op[i][Operation1], op[i][Operation0]);
if(op[i][ALUOp1] == 0 && op[i][ALUOp0] == 0){
printf("row1 ");
if(op[i][Operation2] != 0 || op[i][Operation1] != 1 || op[i][Operation0] != 0){
printf("CONFLICTS WITH TABLE! ");
}
}
if(op[i][ALUOp1] == 0 && op[i][ALUOp0] == 1){
printf("row2 ");
if(op[i][Operation2] != 1 || op[i][Operation1] != 1 || op[i][Operation0] != 0){
printf("CONFLICTS WITH TABLE! ");
}
}
if(op[i][ALUOp1] == 1 && op[i][F3] == 0 && op[i][F2] == 0 && op[i][F1] == 0 && op[i][F0] == 0){
printf("row3 ");
if(op[i][Operation2] != 0 || op[i][Operation1] != 1 || op[i][Operation0] != 0){
printf("CONFLICTS WITH TABLE! ");
}
}
if(op[i][ALUOp1] == 1 && op[i][F3] == 0 && op[i][F2] == 0 && op[i][F1] == 1 && op[i][F0] == 0){
printf("row4 ");
if(op[i][Operation2] != 1 || op[i][Operation1] != 1 || op[i][Operation0] != 0){
printf("CONFLICTS WITH TABLE! ");
}
}
if(op[i][ALUOp1] == 1 && op[i][F3] == 0 && op[i][F2] == 1 && op[i][F1] == 0 && op[i][F0] == 0){
printf("row5 ");
if(op[i][Operation2] != 0 || op[i][Operation1] != 0 || op[i][Operation0] != 0){
printf("CONFLICTS WITH TABLE! ");
}
}
if(op[i][ALUOp1] == 1 && op[i][F3] == 0 && op[i][F2] == 1 && op[i][F1] == 0 && op[i][F0] == 1){
printf("row6 ");
if(op[i][Operation2] != 0 || op[i][Operation1] != 0 || op[i][Operation0] != 1){
printf("CONFLICTS WITH TABLE! ");
}
}
if(op[i][ALUOp1] == 1 && op[i][F3] == 1 && op[i][F2] == 0 && op[i][F1] == 1 && op[i][F0] == 0){
printf("row7 ");
if(op[i][Operation2] != 1 || op[i][Operation1] != 1 || op[i][Operation0] != 1){
printf("CONFLICTS WITH TABLE! ");
}
}
printf("\n");
}
return(0);
}
Mac_3.2.57$cc kmap_so_60848669--how-can-i-find-the-equation-from-this-truth-table-using-k-map-or-qm-method.c
Mac_3.2.57$./a.out
ALUOp1 ALUOp0 F3 F2 F1 F0 Operation210 Notes
0 0 0 0 0 0 010 row1
0 0 0 0 0 1 010 row1
0 0 0 0 1 0 010 row1
0 0 0 0 1 1 010 row1
0 0 0 1 0 0 010 row1
0 0 0 1 0 1 010 row1
0 0 0 1 1 0 010 row1
0 0 0 1 1 1 010 row1
0 0 1 0 0 0 010 row1
0 0 1 0 0 1 010 row1
0 0 1 0 1 0 010 row1
0 0 1 0 1 1 010 row1
0 0 1 1 0 0 010 row1
0 0 1 1 0 1 010 row1
0 0 1 1 1 0 010 row1
0 0 1 1 1 1 010 row1
0 1 0 0 0 0 110 row2
0 1 0 0 0 1 110 row2
0 1 0 0 1 0 110 row2
0 1 0 0 1 1 110 row2
0 1 0 1 0 0 110 row2
0 1 0 1 0 1 110 row2
0 1 0 1 1 0 110 row2
0 1 0 1 1 1 110 row2
0 1 1 0 0 0 110 row2
0 1 1 0 0 1 110 row2
0 1 1 0 1 0 110 row2
0 1 1 0 1 1 110 row2
0 1 1 1 0 0 110 row2
0 1 1 1 0 1 110 row2
0 1 1 1 1 0 110 row2
0 1 1 1 1 1 110 row2
1 0 0 0 0 0 010 row3
1 0 0 0 0 1 011
1 0 0 0 1 0 110 row4
1 0 0 0 1 1 111
1 0 0 1 0 0 000 row5
1 0 0 1 0 1 001 row6
1 0 0 1 1 0 100
1 0 0 1 1 1 101
1 0 1 0 0 0 011
1 0 1 0 0 1 011
1 0 1 0 1 0 111 row7
1 0 1 0 1 1 111
1 0 1 1 0 0 001
1 0 1 1 0 1 001
1 0 1 1 1 0 101
1 0 1 1 1 1 101
1 1 0 0 0 0 110 row3 CONFLICTS WITH TABLE!
1 1 0 0 0 1 111
1 1 0 0 1 0 110 row4
1 1 0 0 1 1 111
1 1 0 1 0 0 100 row5 CONFLICTS WITH TABLE!
1 1 0 1 0 1 101 row6 CONFLICTS WITH TABLE!
1 1 0 1 1 0 100
1 1 0 1 1 1 101
1 1 1 0 0 0 111
1 1 1 0 0 1 111
1 1 1 0 1 0 111 row7
1 1 1 0 1 1 111
1 1 1 1 0 0 101
1 1 1 1 0 1 101
1 1 1 1 1 0 101
1 1 1 1 1 1 101
Mac_3.2.57$
0
FWIW, here is the start of the kmaps (not accurate due to conflicts between table and CKT): Op = o2o1o0
o2:
f1\f0 0 1
p1p0\f3f2 00 01 11 10 p1p2\f3f2 00 01 11 10
00 0 0 0 0 00 0 0 0 0
01 x x x x 01 x x x x
0
11 0 0 x x 11 x 0 x x
10 0 0 x x 10 x 0 x x
p1p0\f3f2 00 01 11 10 p1p2\f3f2 00 01 11 10
00 0 0 0 0 00 0 0 0 0
01 x x x x 01 x x x x
1
11 1 x x 1 11 x x x x
10 1 x x 1 10 x x x x
o1:
f1\f0 0 1
p1p0\f3f2 00 01 11 10 p1p2\f3f2 00 01 11 10
00 1 1 1 1 00 1 1 1 1
01 x x x x 01 x x x x
0
11 1 0 x x 11 x 0 x x
10 1 0 x x 10 x 0 x x
p1p0\f3f2 00 01 11 10 p1p2\f3f2 00 01 11 10
00 1 1 1 1 00 1 1 1 1
01 x x x x 01 x x x x
1
11 1 x x 1 11 x x x x
10 1 x x 1 10 x x x x
o0:
f1\f0 0 1
p1p0\f3f2 00 01 11 10 p1p2\f3f2 00 01 11 10
00 0 0 0 0 00 0 0 0 0
01 x x x x 01 x x x x
0
11 1 0 x x 11 x 1 x x
10 1 0 x x 10 x 1 x x
p1p0\f3f2 00 01 11 10 p1p2\f3f2 00 01 11 10
00 0 0 0 0 00 0 0 0 0
01 x x x x 01 x x x x
1
11 0 x x 1 11 x x x x
10 0 x x 1 10 x x x x
Upvotes: 0
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