Digital-Logic
.pdf
2- bit Comparator
A=B |
F1 = S (0,5,10,15) |
|||||
|
A1 A0 |
|
|
|
|
|
|
|
|
|
|
|
|
B1 B0 |
00 |
01 11 |
10 |
|
||
|
|
|
|
|
|
|
|
00 |
0 |
4 |
12 |
8 |
|
|
|
|
|
|
|
|
|
01 |
1 |
5 |
13 |
9 |
|
|
|
|
|
|
|
|
|
11 |
3 |
7 |
15 |
11 |
|
|
|
|
|
|
|
|
|
10 |
2 |
6 |
14 |
10 |
|
|
|
|
|
|
|
|
A1A0 |
|
00 |
01 |
11 |
10 |
|
|
||||||
1 |
0 |
|
||||
B B |
|
|
|
|
|
|
|
00 |
|
1 |
0 |
0 |
0 |
|
01 |
|
0 |
1 |
0 |
0 |
|
11 |
|
|
|
|
|
|
|
0 |
0 |
1 |
0 |
|
|
10 |
|
0 |
0 |
0 |
1 |
|
|
|
|
|
|
|
F1 = 1 when both numbers, A and B, are equal which happens when all their bits of the same order are identical, i.e. A0 = B0 AND A1 = B1
F1 = (A0ÅB0) • (A1 ÅB1)
© Emil M. Petriu
2- bit Comparator
A<B |
F3 = Σ (1,2,3,6,7,11) |
A1A0 |
|
|
|
|
|
||||
|
A1 A0 |
|
|
|
|
B1B0 |
00 |
01 |
11 |
10 |
|
|
|
|
|
|
00 |
0 |
0 |
0 |
0 |
|
|
B1 B0 |
00 |
01 11 |
10 |
|
|||||||
01 |
1 |
0 |
0 |
0 |
|
||||||
|
00 |
0 |
4 |
12 |
8 |
|
|||||
|
11 |
1 |
1 |
0 |
1 |
|
|||||
|
01 |
1 |
5 |
13 |
9 |
|
|||||
|
10 |
1 |
1 |
0 |
0 |
|
|||||
|
11 |
3 |
7 |
15 |
11 |
|
|||||
|
|
|
|
|
|
|
|||||
|
10 |
2 |
6 |
14 |
10 |
F = A B B |
+ A B |
+ A1A0B0 |
|||
|
|
|
|
|
|
||||||
|
|
|
|
|
|
3 |
0 1 0 |
|
1 1 |
||
© Emil M. Petriu
2- bit Comparator
A>B 
F2 = Σ (4,8,9,12,13,14)
A1A0 |
00 |
01 |
11 |
10 |
|
1 |
0 |
||||
B B |
|
|
|
|
|
|
00 |
0 |
1 |
1 |
1 |
|
01 |
0 |
0 |
1 |
1 |
|
|
|
|
|
|
|
11 |
0 |
0 |
0 |
0 |
|
|
|
|
|
|
|
10 |
0 |
0 |
1 |
0 |
|
|
|
|
|
|
|
A1 A0 |
|
|
|
|
|
|
|
|
||
B1 B0 |
00 |
01 11 |
10 |
||
|
00 |
0 |
4 |
12 |
8 |
|
|
|
|
|
|
01 |
1 |
5 |
13 |
9 |
|
|
|
|
|
|
|
11 |
3 |
7 |
15 |
11 |
|
|
|
|
|
|
|
10 |
2 |
6 |
14 |
10 |
|
|
|
|
|
|
|
F2 = F1 + F3
A1A0 |
|
F1+F3 |
|
|
|
|
|||
B1B0 |
00 |
01 |
11 |
10 |
00 |
1 |
0 |
0 |
0 |
01 |
|
|
|
|
1 |
1 |
0 |
0 |
|
11 |
|
|
|
|
1 |
1 |
1 |
1 |
|
|
|
|
|
|
10 |
1 |
1 |
0 |
1 |
|
|
|
|
|
A1A0 |
|
|
F1 |
|
|
1 |
0 |
00 |
01 |
11 |
10 |
B B |
|
|
|
|
|
|
00 |
1 |
0 |
0 |
0 |
|
01 |
0 |
1 |
0 |
0 |
|
11 |
0 |
0 |
1 |
0 |
|
10 |
0 |
0 |
0 |
1 |
A1A0 |
|
|
F3 |
|
B1B0 |
00 |
01 |
11 |
10 |
00 |
0 |
0 |
0 |
0 |
01 |
1 |
0 |
0 |
0 |
11 |
1 |
1 |
0 |
1 |
10 |
1 |
1 |
0 |
0 |
© Emil M. Petriu
2- bit Comparator |
F1 = (A0ÅB0) • (A1 ÅB1) |
|
|
F2 |
= F1 + F3 |
B1 B0 A1 A0 |
F3 = A0B1B0+A1B1+A1A0B0 |
|
|
|
|
|
A1 |
ÅB1 |
|
|
F1 = (A0ÅB0) • (A1 ÅB1) |
|
A0 ÅB0 |
|
|
|
F2 = F1 + F3 |
|
|
F3 = A0B1B0+A1B1+A1A0B0 |
© Emil M. Petriu
3-to-8 Decoder
|
A B C |
F0 |
F1 |
F2 |
F3 |
F4 |
F5 |
F6 |
F7 |
||
(0) |
|
|
|
|
|
|
|
|
|
|
|
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
|
(1) |
0 |
0 |
1 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
(2) |
0 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
(3) |
0 |
1 |
1 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
(4) |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
(5) |
1 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
(6) |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
(7) |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
|
|
|
|
|
|
|
|
|
|
|
|
© Emil M. Petriu
A |
B |
C |
F0
F1
F2
F3
F4
F5
F6
F7
3-to-8 Decoder (74 138)
A B C E F0 F1 F2 F3 F4 F5 F6 F7
(x)x x x 1 1 1 1 1 1 1 1 1
(0) |
0 |
0 |
0 |
0 0 1 1 1 1 1 1 1 |
|||||||
(1) |
0 |
0 |
1 |
0 1 0 1 1 1 1 1 1 |
|||||||
(2) 0 1 0 0 1 1 0 1 1 1 1 1 |
|||||||||||
(3) 0 1 1 0 1 1 1 0 1 1 1 1 |
|||||||||||
(4) 1 0 0 0 1 1 1 1 0 1 1 1 |
|||||||||||
(5) 1 0 1 0 1 1 1 1 1 0 1 1 |
|||||||||||
(6) |
1 |
1 |
0 |
0 1 |
1 |
1 |
1 |
1 |
1 |
0 |
1 |
(7) 1 |
1 |
1 |
0 1 |
1 1 1 1 1 1 0 |
|||||||
© Emil M. Petriu
E |
A |
B |
C |
F0
F1
F2
F3
F4
F5
F6
F7
BCD-TO-7 SEGMENT DECODER
|
|
|
S1 |
|
|
|
|
|
S6 |
S7 |
S2 |
|
|
|
|
|
|
|
|
|
|
|
S5 |
S4 |
S3 |
|
|
|
|
|
|
|
|
|
S7 |
S6 |
S5 |
S4 |
S3 |
S2 |
S1 |
|
|
|
7 SEGMENT |
|
||
BCD
|
|
|
|
|
|
|
|
B3 |
B2 |
B1 |
B0 |
||||
|
|
|
|
|
|
|
|
B3 B2 B1 B0
_________________________
(0) |
0 |
0 |
0 |
0 |
(1) |
0 |
0 |
0 |
1 |
(2) |
0 |
0 |
1 |
0 |
(3) |
0 |
0 |
1 |
1 |
(4) |
0 |
1 |
0 |
0 |
(5) |
0 |
1 |
0 |
1 |
(6) |
0 |
1 |
1 |
0 |
(7) |
0 |
1 |
1 |
1 |
(8) |
1 |
0 |
0 |
0 |
(9) |
1 |
0 |
0 |
1 |
(x) |
1 |
0 |
1 |
0 |
(x) |
1 |
0 |
1 |
1 |
(x) |
1 |
1 |
0 |
0 |
(x) |
1 |
1 |
0 |
1 |
(x) |
1 |
1 |
1 |
0 |
(x) |
1 |
1 |
1 |
1 |
|
B3 B2 |
|
|
|
|
|
|
|
|
||
B1 B0 |
00 |
01 11 |
10 |
||
|
|
|
|
|
|
00 |
0 |
4 |
x |
8 |
|
|
|
|
|
|
|
01 |
1 |
5 |
x |
9 |
|
|
|
|
|
|
|
11 |
3 |
7 |
x |
x |
|
|
|
|
|
|
|
10 |
2 |
6 |
x |
x |
|
|
|
|
|
|
|
“Don’t Care” states/situations. As it is expected that these states are never going to occur, then we may just as well use them as fill-in “1s” in a Karnaugh map if this helps to make larger loopings
© Emil M. Petriu
BCD-to-7 segment
B3 B2 B1 B0
_________________________
(0) |
0 |
0 |
0 |
0 |
(1) |
0 |
0 |
0 |
1 |
(2) |
0 |
0 |
1 |
0 |
(3) |
0 |
0 |
1 |
1 |
(4) |
0 |
1 |
0 |
0 |
(5) |
0 |
1 |
0 |
1 |
(6) |
0 |
1 |
1 |
0 |
(7) |
0 |
1 |
1 |
1 |
(8) |
1 |
0 |
0 |
0 |
(9) |
1 |
0 |
0 |
1 |
(x) |
1 |
0 |
1 |
0 |
(x) |
1 |
0 |
1 |
1 |
(x) |
1 |
1 |
0 |
0 |
(x) |
1 |
1 |
0 |
1 |
(x) |
1 |
1 |
1 |
0 |
(x) |
1 |
1 |
1 |
1 |
|
S1 |
|
|
S1 |
|
|
S1 |
|
|
S1 |
|
|
S1 |
|
S6 |
S7 |
S2 |
S6 |
S7 |
S2 |
S6 |
S7 |
S2 |
S6 |
S7 |
S2 |
S6 |
S7 |
S2 |
|
|
|
|
|
|
|
|
|
|
|||||
S5 |
S4 |
S3 |
S5 |
S4 |
S3 |
S5 |
S4 |
S3 |
S5 |
S4 |
S3 |
S5 |
S4 |
S3 |
|
|
|
|
|
|
|
|
|
|
|||||
|
S1 |
|
|
S1 |
|
|
S1 |
|
|
S1 |
|
|
S1 |
|
S6 |
S7 |
S2 |
S6 |
S7 |
S2 |
S6 |
S7 |
S2 |
S6 |
S7 |
S2 |
S6 |
S7 |
S2 |
|
|
|
|
|
|
|
|
|
|
|||||
S5 |
S4 |
S3 |
S5 |
S4 |
S3 |
S5 |
S4 |
S3 |
S5 |
S4 |
S3 |
S5 |
S4 |
S3 |
|
|
|
|
|
|
|
|
|
|
|
S4 = 0+2+3+5+6+8+9 |
S1 = 0+2 +3+5+6+7+8+9 |
S5 = 0+2+6+8 |
S2 = 0+1+2+3+4+7+8+9 |
S6 = 0+4+5+6+8+9 |
|
|
S3 = 0+1+3+4+5+6+7+8+9 |
S7 = 2+3+4+5+6+8+9 |
|
© Emil M. Petriu
BCD-to-7 segment
S1 = 0+2 +3+5 +6+7+8+9
|
B3 B2 |
|
|
|
|
S1 |
|
|
||
B1 B0 |
|
00 |
01 11 |
10 |
||||||
|
00 |
|
1 |
0 |
|
|
|
|
|
|
|
|
|
x |
1 |
|
|||||
01 |
|
|
|
|
|
|
|
|
||
|
0 |
1 |
|
|
x |
1 |
|
|||
11 |
|
|
|
|
|
|
|
|
||
|
|
1 |
1 |
|
|
x |
x |
|
||
|
|
|
|
|||||||
10 |
|
|
|
|
|
|
|
|
|
|
|
|
1 |
1 |
|
|
x |
x |
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
B3 B2 |
|
|
|
|
|
|
|
|
||
B1 B0 |
00 |
01 |
11 |
10 |
|
|
|
|
|
|
|
00 |
0 |
4 |
x |
8 |
|
|
|
|
|
|
|
01 |
1 |
5 |
x |
9 |
|
|
|
|
|
|
|
11 |
3 |
7 |
x |
x |
|
|
|
|
|
|
|
10 |
2 |
6 |
x |
x |
|
|
|
|
|
|
|
S1 = |
B3 |
+ |
|
|
|
|
+ |
B1 |
|
|
|
B2B0 |
|
|
|
||||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
S2 = |
|
+ B2B1 + |
B2B0 |
B3 |
|||||||||
S2 = 0+1+2+3 +4+7+8+9
|
B3 B2 |
|
|
S2 |
|
|
|||
B1 B0 |
00 |
01 11 |
10 |
|
|||||
|
00 |
|
1 |
1 |
|
|
|
|
|
|
|
|
x |
1 |
|
||||
01 |
|
|
|
|
|
|
|
|
|
|
1 |
0 |
|
|
x |
1 |
|
||
11 |
|
|
|
|
|
|
|
|
|
|
1 |
1 |
|
|
x |
x |
|
||
10 |
|
|
|
|
|
|
|
|
|
|
1 |
0 |
|
|
x |
x |
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
+ B2 + B1B0 + B1B0
© Emil M. Petriu
BCD-to-7 segment |
|
|
|
B3 B2 |
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
B1 B0 |
00 |
01 |
11 |
10 |
|
|
|
|
||
|
|
|
|
|
|
00 |
0 |
4 |
|
x |
8 |
|
|
|
|
|
|
|
|
|
|
01 |
1 |
5 |
|
x |
9 |
|
|
|
|
S3 = 0+1+3+4+5+6+7+8+9 |
11 |
3 |
7 |
|
x |
x |
|
|
|
|
|||||
10 |
2 |
6 |
|
x |
S4 = 0+2+3+5+6+8+9 |
||||||||||
|
|
|
|
|
|
|
x |
|
|
|
|
||||
B3 B2 |
|
S3 |
|
|
|
|
|
|
|
|
B3 B2 |
|
|
S4 |
|
B1 B0 |
00 |
01 11 |
10 |
|
|
|
|
|
|
B1 B0 |
00 |
01 11 |
10 |
||
00 |
1 |
1 |
x |
1 |
|
|
|
|
|
|
00 |
1 |
0 |
x |
1 |
01 |
|
|
|
|
|
|
|
|
|
|
|||||
1 |
1 |
x |
1 |
|
|
|
|
|
|
01 |
0 |
1 |
x |
1 |
|
11 |
1 |
1 |
x |
x |
|
|
|
|
|
|
11 |
1 |
0 |
x |
x |
10 |
0 |
1 |
x |
x |
|
|
|
|
|
|
10 |
1 |
1 |
x |
x |
|
|
|
|
|
|
|
|
|
|
|
|||||
S3 = B3 + |
B1B0 + B1 |
+ |
B2 |
S4 = |
B3 + |
B2B0 + B2B1 + B2B1B0 + B1B0 |
|||||||||
|
|
|
|
|
|
||||||||||
© Emil M. Petriu