2. Realize the following function F(4,B,C,D) = E(1,2, 5, 6, 7,11) using a (a) 4-to-1 multiplexer, and draw the logic diagram. (b) 8-to-1 multiplexer, and draw the logic diagram. You may use external gates if needed.

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2. Realize the following function
F(A,B,C,D) = (1,2, 5, 6,7,11)
using a
(a) 4-to-1 multiplexer, and draw the logic diagram.
(b) 8-to-1 multiplexer, and draw the logic diagram.
You may use external gates if needed.
Transcribed Image Text:2. Realize the following function F(A,B,C,D) = (1,2, 5, 6,7,11) using a (a) 4-to-1 multiplexer, and draw the logic diagram. (b) 8-to-1 multiplexer, and draw the logic diagram. You may use external gates if needed.
Example #3
Example #2
Realize the following Boolean function using minimal number of
external gates and an 8-to-1 multiplexer.
Realize the following Boolean function using minimal number of
external gates and a 4-to-1 multiplexer.
ABCD F
F (A, B, C, D) = E(1, 3, 4, 11, 12, 13, 14, 15)
0 0 0 0 0 F-D
0 0 0 1 1
8x1 MUX
F (x, y, z) = £(1, 2, 6, 7)
4 x1 MUX
C
So
0 1
0 1
F = D
1 1
В
So
x y z|F
A
S2
1
0 1
F = D
S1
1 0 10
F = z
1
0 1
1 1
1 1 10
F=0
Do
F
F
2.
1
F= z'
10 0
0 0
0 0 10
F = 0
3
1
1
z'
1
1
4
1
F = 0
2.
1
1
0 1 11
0
1
5
F = D
1
1
6.
1
3
01 F=1
1
1
1 1 1 1
1
1 0
0 1
F= 1
1
10 11
01 F=1
1
1 1
1
1 1 1 1
(a) Truth table
(b) Multiplexer implementation
F = 1
Transcribed Image Text:Example #3 Example #2 Realize the following Boolean function using minimal number of external gates and an 8-to-1 multiplexer. Realize the following Boolean function using minimal number of external gates and a 4-to-1 multiplexer. ABCD F F (A, B, C, D) = E(1, 3, 4, 11, 12, 13, 14, 15) 0 0 0 0 0 F-D 0 0 0 1 1 8x1 MUX F (x, y, z) = £(1, 2, 6, 7) 4 x1 MUX C So 0 1 0 1 F = D 1 1 В So x y z|F A S2 1 0 1 F = D S1 1 0 10 F = z 1 0 1 1 1 1 1 10 F=0 Do F F 2. 1 F= z' 10 0 0 0 0 0 10 F = 0 3 1 1 z' 1 1 4 1 F = 0 2. 1 1 0 1 11 0 1 5 F = D 1 1 6. 1 3 01 F=1 1 1 1 1 1 1 1 1 0 0 1 F= 1 1 10 11 01 F=1 1 1 1 1 1 1 1 1 (a) Truth table (b) Multiplexer implementation F = 1
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