1) Given a 2x4 decoder which is always enabled and whose most significant selection line S1 is
connected to channel A, and the least significant selection line S0 connected to B. This
decoder’s outputs are connected to their corresponding inputs of a 4-to-1 MUX whose S1 is
connected to channel C and its S0 is connected to channel D. Find the expression of the MUX
output F(A,B,C,D).
Solution:
General Guidelines:
1- Draw the circuit.
2- Determine its type (combinational or sequential).
3- If combinational, build the Truth Table of the circuit or find a quick shortcut based on the
behavior of the components used.
4- If sequential, draw the state diagram.
For this question, the circuit is drawn as above and it is a combinational circuit since it
contains no flip-flops.
The 2x4 decoder will always produce the minterms of its inputs. The MUX output
depends on its selection lines.
Now, try using a truth table instead.
The truth table is provided as follows:
A
B
C
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2)
D
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
F