Magnitude Comparator

1
Magnitude Comparator

• Module M5.2
• Section 6.1

2
4-Bit Equality Detector
A3..0
Equality Detector
A_EQ_B
B3..0
3
Magnitude Comparator
A_LT_B
A3..0
Magnitude Detector
A_EQ_B
B3..0
A_GT_B
4
Magnitude Comparator
How can we find A_GT_B?
How many rows would a truth table have?
28 256!
5
Magnitude Comparator
Find A_GT_B
Because A3 gt B3 i.e. A3 !B3 1
If A 1001 and B 0111 is A gt B? Why?
Therefore, one term in the logic equation for
A_GT_B is A3 !B3
6
Magnitude Comparator
A_GT_B A3 !B3 ..
Because A3 B3 and A2 gt B2 i.e. C3
1 and A2 !B2 1
If A 1101 and B 1011 is A gt B? Why?
Therefore, the next term in the logic equation
for A_GT_B is C3 A2 !B2
7
Magnitude Comparator
A_GT_B A3 !B3 C3 A2
!B2 ..
Because A3 B3 and A2 B2 and
A1 gt B1 i.e. C3 1 and C2 1 and
A1 !B1 1
If A 1010 and B 1001 is A gt B? Why?
Therefore, the next term in the logic equation
for A_GT_B is C3 C2 A1 !B1
8
Magnitude Comparator
A_GT_B A3 !B3 C3 A2
!B2 C3 C2 A1 !B1
..
Because A3 B3 and A2 B2 and
A1 B1 and A0 gt B0 i.e.
C3 1 and C2 1 and C1 1 and A0 !B0 1
If A 1011 and B 1010 is A gt B? Why?
Therefore, the last term in the logic equation
for A_GT_B is C3 C2 C1 A0 !B0
9
Magnitude Comparator
A_GT_B A3 !B3 C3 A2
!B2 C3 C2 A1 !B1
C3 C2 C1 A0 !B0
10
Magnitude Comparator
Find A_LT_B
A_LT_B !A3 B3 C3 !A2
B2 C3 C2 !A1 B1
C3 C2 C1 !A0 B0
11
ABEL Program
MODULE magcomp4 TITLE '4-BIT COMPARATOR, R.
Haskell, 9/21/02 DECLARATIONS " INPUT PINS
" A3..A0 PIN 6,7, 11, 5 A A3..A0 B3..B0 PIN
72, 71, 66, 70 B B3..B0 " OUTPUT PINS
" A_EQ_B PIN 36 A_LT_B PIN 37 A_GT_B PIN
35 C3..C0 NODE C C3..C0
12
ABEL Program (cont.)
EQUATIONS C !(A B) A_EQ_B C0 C1 C2
C3 A_GT_B A3 !B3 C3 A2 !B2 C3
C2 A1 !B1 C3 C2 C1 A0 !B0 A_LT_B
!A3 B3 C3 !A2 B2 C3 C2 !A1
B1 C3 C2 C1 !A0 B0
13
ABEL Program (cont.)
test_vectors (A, B -gt A_EQ_B, A_LT_B,
A_GT_B) 0, 0 -gt 1, 0, 0 2, 5 -gt 0, 1,
0 10, 12 -gt 0, 1, 0 7, 8 -gt 0, 1,
0 4, 2 -gt 0, 0, 1 6, 6 -gt 1, 0, 0 1,
7 -gt 0, 1, 0 5, 13 -gt 0, 1, 0 12, 0 -gt
0, 0, 1 6, 3 -gt 0, 0, 1 9, 9 -gt 1, 0,
0 12, 13 -gt 0, 1, 0 7, 0 -gt 0, 0,
1 4, 1 -gt 0, 0, 1 3, 2 -gt 0, 0,
1 15, 15 -gt 1, 0, 0 END
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
TTL Comparators
18
Cascading two 74LS85s
19
Question
P_GT_Q P_EQ_Q P_LT_Q
Draw a logic circuit for what is in the green box.