Example 3: Design a logic circuit whose output is HIGH only when a majority of the inputs A, B and C are HIGH.
Example 3: Design a logic circuit whose output is HIGH only when a majority of the inputs A, B and C are HIGH.
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Example 3: Design a logic circuit whose output is HIGH only when a majority of
the inputs A, B and C are HIGH.
Solution:
Step 1 Truth Table:
There are three inputs (A, B, and C) and one output, F.
The truth table is then obtained from problem definition and is shown in Table.
ABCF
0 00 0
0010
0 100
0 111
10 00
1011
1101
1 111
|
Step 2 Minimization: Output, F in the truth table is simplified using a K-map.
The output equation is obtained as F=AB+ C(A+B)
1.
AB
00
01
F=AB+AC+BC
OR
1
F-AB+ C(A+B)
10
1
Step 3 Logic diagram or Schematic: Using cquations of Step 2, the schematic
is drawn as shown in Figure below.
B.
C
v/o
Example 4: Design a combinational circuit with three inputs, x, y and z, and the
three outputs, A, B, and C. when the binary input is 0, 1, 2, or 3, the binary output
is one greater than the input. When the binary input is 4, 5, 6, or 7, the binary
output is one less than the input.
Solution:
Step 1 Truth Table:
-There are three inputs (x, y, and z) and three outputs (A, B, and C).
-The truth table is then obtained from problem definition( specifications of the
circuit) and is shown in Table below:
xy z ABC
000001
00 10
01001 1
0 1 11 00
10 0011
10 1 1 00
|110 10 1
11 1 1 10
Step 2 Minimization: Output, A, B and C in the truth table is simplified
using a K-map. The output equation is obtained as:
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