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Digital Electronics
Table 7.2 Functional table of IC 7485 or IC 4585.
Comparison inputs
Cascading inputs
Outputs
A 3 ,B 3
A 2 ,B 2
A 1 ,B 1
A 0 ,B 0
A > B
A < B
A = B
A > B
A < B
A = B
A 3 > B 3
X
X
X
X
X
X
HIGH
LOW
LOW
A 3 < B 3
X
X
X
X
X
X
LOW
HIGH
LOW
A 3 = B 3
A 2 > B 2
X
X
X
X
X
HIGH
LOW
LOW
A 3 = B 3
A 2 < B 2
X
X
X
X
X
LOW
HIGH
LOW
A 3 = B 3
A 2 = B 2
A 1 > B 1
X
X
X
X
HIGH
LOW
LOW
A 3 = B 3
A 2 = B 2
A 1 < B 1
X
X
X
X
LOW
HIGH
LOW
A 3 = B 3
A 2 = B 2
A 1 = B 1
A 0 > B 0
X
X
X
HIGH
LOW
LOW
A 3 = B 3
A 2 = B 2
A 1 = B 1
A 0 < B 0
X
X
X
LOW
HIGH
LOW
A 3 = B 3
A 2 = B 2
A 1 = B 1
A 0 = B 0
HIGH
LOW
LOW
HIGH
LOW
LOW
A 3 = B 3
A 2 = B 2
A 1 = B 1
A 0 = B 0
LOW
HIGH
LOW
LOW
HIGH
LOW
A 3 = B 3
A 2 = B 2
A 1 = B 1
A 0 = B 0
LOW
LOW
HIGH
LOW
LOW
HIGH
A 3 = B 3
A 2 = B 2
A 1 = B 1
A 0 = B 0
X
X
HIGH
LOW
LOW
HIGH
A 3 = B 3
A 2 = B 2
A 1 = B 1
A 0 = B 0
HIGH
HIGH
LOW
LOW
LOW
LOW
A 3 = B 3
A 2 = B 2
A 1 = B 1
A 0 = B 0
LOW
LOW
LOW
HIGH
HIGH
LOW
Solution
Let A AA 1 A 0 and B BB 1 B 0 be the two numbers. If X, Y and Z represent the conditions A = BB A > B
and A < B respectively (that is, X = 1, Y = 0 and Z = 0 for A =B; X= 0, Y = 1 and Z = 0 for
A > B; and X = 0, Y = 0 and Z = 1 for A < B), then expressions for X, Y and Z can be written as
follows:
X = x 1 .x 0 where x 1 = A 1 B 1 + A 1 B 1 and x 0 = A 0 B 0 + A 0 B 0
Y = A 1 B 1 + x 1 A 0 B 0
Z = A 1 B 1 + x 1 A 0 B 0
Figure 7.38 shows the logic diagram of the two-bit comparator.
Example 7.9
Hardware-implement a three-bit magnitude comparator having one output that goes HIGH when the
two three-bit numbers are equal. Use only NAND gates.
Solution
The equivalence condition of the two three-bit numbers is given by the equation X = x 2 .x 1 .x 0 , where
x 2 = A 2 B 2 + A 2 B 2 , x 1 = A 1 B 1 + A 1 B 1 and x 0 = A 0 B 0 + A 0 B 0 .
Figure 7.39 shows the logic diagram. x 2 , x 1 and x 0 are respectively given by EX-NOR operation of
(A 2 , B 2 , (A 1 , B 1 and (A 0 , B 0 . These are then ANDed to get X.