Tuesday, 8 March 2016

Priority Encoder


Definition
A priority encoder is an combinational circuit that implements the priority function.It is often used in scheduling interrupt requests.If two or more interrupts arrive at the same time, the interrupt having the highest priority will take precedence and get serviced first.
Block Diagram
Block Diagram of Priority Encoder
General Equation
  •  A 4 x 2 priority encoder has 4 inputs & 2 outputs (22 = 4). 
  •   In general, an n x m priority encoder has n inputs and m (2m = n )outputs. 
Truth Table
Inputs
Outputs
D3
D2
D1
D0
Y1
Y0
V
0
0
0
0
x
x
0
0
0
0
1
0
0
1
0
0
1
x
0
1
1
0
1
x
x
1
0
1
1
x
x
x
1
1
1

Explanation 

The above Truth Table represents a 4 x 2 priority encoder.

Since the priority encoder deals with priority signals assigned to input lines, only  one input is in ON (Binary - 1) state at any point of time and the other inputs are in OFF (Binary - 0) state. So only 5 (Five) combinations of inputs are possible(including invalid inputs) as shown in Truth Table.

Here, D0 is assumed as Low Priority Input and D3 is assumed as High Priority Input. There is Valid Output (V) that designates the validity of the servicing the input signal. If V=0, the inputs are invalid and if V=1, the inputs are valid. 

When the truth values of all the inputs (D0 through D1) are '0', the outputs are not determined. So, we mark a  'x' (don't care) value. 

When D0 = 1,  the outputs Y0 & Y1 are '0' - means that it is a low priority input  compared to D1,D2 &D3. 

When D1 = 1, the output Y0=1 & Y1 =0 - means that its priority > D0 and less than D2 & D3.

When D2 = 1, the output Y0=0 & Y1 =1 - meaning that its priority > D1,D0 and less than  D3. 
When D3  = 1, the outputs Y0=1 & Y1=1  - meaning that it is a high priority input compared to D0, D2 &D3.

Design of Logic Circuit for 4 x 2 priority encoder 

The Logic Circuit for 4X2 Priority encoder can be done using Karnaugh Map (K-Map).

Since there are two outputs (excluding V output), two 4 x 4 K-Maps are possible( one for the output Y0 & the second for the output Y1). 

K-Map for output Y1




K-Map Explanation for output Y1
Inputs for D3D2D1D0
Entry in K-Map for output Y1
Reason
0000
x
No output is generated when all inputs are 0
0001
0
Output 0 is generated for input D0 – No need to consider the truth values of other inputs.
0011
0
Output 0 is generated for input D1 – No need to consider the truth values of other inputs.
0010
0
Output 0 is generated for input D1 – No need to consider the truth values of other inputs.
0100
1
Output 1 is generated for input D2 – No need to consider the truth values of other inputs.
0101
1
Output 1 is generated for input D2 – No need to consider the truth values of other inputs.
0111
1
Output 1 is generated for input D2 – No need to consider the truth values of other inputs.
0110
1
Output 1 is generated for input D2 – No need to consider the truth values of other inputs.
1100
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.
1101
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.
1111
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.
1110
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.
1000
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.
1001
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.
1011
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.
1010
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.


Expression for O1 derived from K-Map

  For Minterms showing in (i) : O1 = D3
 For Minterms showing in (ii) : O1 = D2

Final Output for O1 = D2 + D3 --------  (A)
K-Map for output O0

K-Map Explanation for output O0
Inputs for D3D2D1D0
Entry in K-Map for output O0
Reason
0000
x
No output is generated when all inputs are 0
0001
0
Output 0 is generated for input D0 – No need to consider the truth values of other inputs.
0011
0
Output 0 is generated for input D1 – No need to consider the truth values of other inputs.
0010
1
Output 1 is generated for input D1 – No need to consider the truth values of other inputs.
0100
1
Output 1 is generated for input D2 – No need to consider the truth values of other inputs.
0101
0
Output 0 is generated for input D2 – No need to consider the truth values of other inputs.
0111
0
Output 0 is generated for input D2 – No need to consider the truth values of other inputs.
0110
0
Output 0 is generated for input D2 – No need to consider the truth values of other inputs.
1100
1
Output 1 is generated for input D2 – No need to consider the truth values of other inputs.
1101
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.
1111
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.
1110
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.
1000
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.
1001
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.
1011
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.
1010
1
Output 1 is generated for input D3 – No need to consider the truth values of other inputs.

Expression for O0 derived from K-Map

 For Minterms showing in (i) : O0 = D1D2
 For Minterms showing in (ii) : O1 = D3

Final Output for O0 = D3 + D1D2 --------  (B)

Circuit Diagram

 Using (A) & (B) we can design the Priority Encoder circuit using AND gates and OR gates.

              

                                    -------  x --------





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