A decoder is a digital circuit that takes binary inputs and selects one of multiple outputs. It has N inputs and 2N outputs. The decoder decodes the binary value on its N inputs and activates exactly one output corresponding to that input combination. Decoders generate all possible combinations or "minterms" of the input variables.

1. LOGIC DESIGN
Decoders

2. 
A decoder has
N inputs
2N outputs


N
A decoder selects one of 2 outputs by decoding
the binary value on the N inputs.
The decoder generates all of the minterms of the
N input variables.
Exactly one output will be active for each
combination of the inputs.

3. Out0
B
I0
Out1
A
I1
Out2
Out3
msb
W
X
Y
Z
Active-high outputs
W = A'.B'
X = A.B'
Y = A'.B
Z = A.B

4. Out0
B
I0
Out1
A
I1
Out2
Out3
msb
W
X
Y
Z
Active-low outputs
W = (A'.B')'
X = (A.B')'
Y = (A'.B)'
Z = (A.B)'

5. msb

6. 3-to-8 Decoder in VHDL

7. 3-to-8 Decoder in VHDL

8. Decoder with Enable
B
A
high-level
enable
Out3
W
X
Y
Z
Out0
I0
I1
Out1
Out2
Enable
En
B
W
X
Y
Z
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
disabled
A
1
enabled
En
1
1
0
0
0
1
0
x
x
0
0
0
0

9. Decoder with Enable
B
A
low-level
enable
Out3
W
X
Y
Z
Out0
I0
I1
Out1
Out2
Enable
En
B
W
X
Y
Z
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
disabled
A
0
enabled
En
1
1
0
0
0
1
1
x
x
0
0
0
0

10. 2-to-4 Decoder with Enable in VHDL

11. Exercise:
Design a 4-to-16 decoder using
2-to-4 decoders only.