Comparators

1
Comparators

• Combinational Design

2
Comparators

• Equality and Magnitude Comparators
• TTL Comparators
• Comparator Networks
• Cascading 1-bit Comparators

3
Equality Comparator
XNOR
X Y Z 0 0 1 0 1 0 1 0 0 1 1 1
X
Z
Y
Z !(X Y)
4
4-Bit Equality Comparator
FIELD A A0..3 FIELD B B0..3 FIELD C
C0..3
5
4-bit Equality Detector
A3..0
Equality Detector
A_EQ_B
B3..0
6
4-bit Magnitude Comparator
A_LT_B
A3..0
Magnitude Detector
A_EQ_B
B3..0
A_GT_B
7
Magnitude Comparator
How can we find A_GT_B?
How many rows would a truth table have?
28 256!
8
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
9
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
10
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
11
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
12
Magnitude Comparator
A_GT_B A3 !B3 C3 A2
!B2 C3 C2 A1 !B1
C3 C2 C1 A0 !B0
13
Magnitude Comparator
Find A_LT_B
A_LT_B !A3 B3 C3 !A2
B2 C3 C2 !A1 B1
C3 C2 C1 !A0 B0
14
Comparators

• Equality and Magnitude Comparators
• TTL Comparators
• Comparator Networks
• Cascading 1-bit Comparators

15
TTL Comparators
16
Cascading two 74LS85s
17
Comparators

• Equality and Magnitude Comparators
• TTL Comparators
• Comparator Networks
• Cascading 1-bit Comparators

18
1-Bit Magnitude Comparator
19
4-Bit Magnitude Comparator
X Y 1101 0110 1110 1011 1011
1011 0101 0111 1010 1011
gt 1
eq 1
lt 1
20
Tree comparator network