Page 88 - DCAP108_DIGITAL_CIRCUITS_AND_LOGIC_DESIGNS

Unit 5: Combinational Circuits

Notes
Figure 5.6: A 4-to-2 Binary Encoder

w w w w y y
3 2 1 0 1 0
0 0 0 1 0 0
0 0 1 0 0 1
0 1 0 0 1 0
1 0 0 0 1 1

(a) Truth table

(b) Circuit

Draw a logic diagram for 8-to-2 binary encoder.

5.3.2 Priority Encoder
Another useful class of encoders is based on the priority of input signals. In a priority encoder each
input has a priority level associated with it. The encoder outputs indicate the active input that has
the highest priority. When an input with a high priority is asserted, the other inputs with lower
priority are ignored. The truth table for a 4-to-2 priority encoder is shown in Figure 5.7. It
assumes that w0 has the lowest priority and w3 the highest. The outputs y1 and y0 represent
the binary number that identifies the highest priority input set to 1. Since it is possible that
none of the inputs is equal to 1, an output, z, is provided to indicate this condition. It is set
to 1 when at least one of the inputs is equal to 1. It is set to 0 when all inputs are equal to 0.
Figure 5.7: Truth Table for a 4-to-2 Priority Encoder

w 3 w 2 w 1 w 0 y 1 y 0 z
0 0 0 0 d d 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

The outputs y1 and y0 are not meaningful in this case, and hence the first row of the truth table can
be treated as a don’t-care condition for y1 and y0. The behaviour of the priority encoder is most
easily understood by first considering the last row in the truth table. It specifies that if input w3
is 1, then the outputs are set to y1y0 = 11. Because w3 has the highest priority level, the values of
inputs w2, w1, and w0 do not matter. To reflect the fact that their values are irrelevant, w2, w1, and
w0 are denoted by the symbol x in the truth table. The second-last row in the truth table stipulates
that if w2 = 1, then the outputs are set to y1y0 = 10, but only if w3 = 0. Similarly, input w1 causes

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