Prof Jess Role @UEAB 2008. A decoder is a circuit which takes an n- bitnumber as input and uses it to select (set to1) exactly one of its 2n outputs Decoders

Prof Jess Role @UEAB 2008


• A decoder is a circuit which takes an n-bitnumber as input and uses it to select (set to1) exactly one of its 2n outputs

Decoders



3 input to 8 output decoderE B2 B1 B0 Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q70 0 0 0 0 1 1 1 1 1 1 10 0 0 1 1 0 1 1 1 1 1 10 0 1 0 1 1 0 1 1 1 1 10 0 1 1 1 1 1 0 1 1 1 10 1 0 0 1 1 1 1 0 1 1 10 1 0 1 1 1 1 1 1 0 1 10 1 1 0 1 1 1 1 1 1 0 10 1 1 1 1 1 1 1 1 1 1 01 X X X 1 1 1 1 1 1 1 1

B0

B1

B2

E

Q0Q1Q2Q3Q4Q5Q6Q7


EncodersAn encoder performs the opposite function to a decoder,

it produces a binary output that indicates which input is active.

There are often PRIORITY encoders because they encode the most significant input.

Eg. A 4 input priority encoder.D0 D1 D2 D3 Q0 Q1 V0 0 0 0 0 0 0 1 0 0 0 0 0 1X 1 0 0 1 0 1 X X 1 0 0 1 1X X X 1 1 1 1

D0

D1

D2

D3

Q0

Q1

V

DataInputs

EncodedOutputs

OutputValid


Decoder: input code word, enable inputs, mapping to output code word


Display requires BCD to 7-segment decoder


2-to-4 decoder:EN=1, I0=1, I1=0 activates Y1


Truth table for 2-to-4 binary decoder


Shaft encoder (Gray code)


DIP for Gray code from mechanical encoding disk


Signal naming conventions74x138 3-to-8 decoder

G must be 100 to decode


Logic diagram74x138 3-to-8 decoder


Truth table74x138 3-to-8 decoder


Logic symbols for 74x138 3-to-8 decoder


5-to-32 Decodercascading

74x138 3-to-8 decoders


G input to construct a 4-to-16 decoder using74x138 3-to-8 decoder


ENCODERS6.5


Binary Encoders

For n=3 2n=8

Input: I0, I1, … I7

Output: Y0, Y1, Y2

If IY=1 Y2Y1Y0=Y


Binary encoder


Request encoder

Only one input signal can be active at a time


Logic equations for a priority encoder

H7 = I7

H6 = I6•I7’

H5 = I5•I6’•I7’

…

Then the outputs are generated bybinary encoding of the H signals(only one of which can be High).


Logic symbol for a generic8-input priority encoder

If I5, I2, and I0 are on, the output is 101


74x148 8-Input Priority Encoder

Active-low I/O

Enable Input

“Got Something”

Enable Output


Truth table for a 74x148 8-input priority encoder

Inverted inputs:only highestLOW bitmatters


Truth table for a 74x148 8-input priority encoder

Note Got Something (GS) and Equal (EQ_L) outputs.


Cascading Priority Encoders

32-input priority encoder


Next: Three-state Devices,Multiplexers and Demultiplexers, EXORs

Summary

Decoders map an n-bit signal to one of 2n signals.

Encoders map one of 2n signals to an n-bit signal. Some encoders can only have one input line active. Priority encoders can have several.

Most MSI modules have additional control I/O lines.Many eight-bit SSI devices can be combined for wider words.



Comparators

A comparator is a circuit which compares two input words and produces 1 if they are equal and 0 if they are not equal.

Based on the Exclusive-OR gate, which returns 0 if its inputs are equal and 1 if they are unequal.

A NOR gate decides whether to return 1 for equality or 0 for inequality.



ComparatorsA B EQL LES GTR

A2 A1 B2 B1 A=B A<B A>B0 0 0 0 1 0 00 0 0 1 0 1 00 0 1 0 0 1 00 0 1 1 0 1 00 1 0 0 0 0 10 1 0 1 1 0 00 1 1 0 0 0 1 (NB Bits reversed)0 1 1 1 0 1 0 (A2 & B2 are LSBs)1 0 0 0 0 0 11 0 0 1 0 1 01 0 1 0 1 0 01 0 1 1 0 1 01 1 0 0 0 0 11 1 0 1 0 0 11 1 1 0 0 0 11 1 1 1 1 0 0


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Prof Jess Role @UEAB 2008. A decoder is a circuit which takes an n- bitnumber as input and uses it to select (set to1) exactly one of its 2n outputs Decoders