Content deleted Content added
→Simple encoder: added image of simple encoder using OR gate |
add ==Implementation==, move circuit after truth table |
||
| (36 intermediate revisions by 25 users not shown) | |||
Line 1:
{{Short description|Digital electronic circuit}}
A '''priority encoder''' is a [[Electronic circuit|circuit]] or [[algorithm]] that compresses multiple [[Binary code|binary]] inputs into a smaller number of outputs, similar to a [[Encoder (digital)|simple encoder]]. The output of a priority encoder is the binary representation of the [[Zero-based numbering|index]] of the [[Bit numbering|most significant]] activated line. In contrast to the simple encoder, if two or more inputs to the priority encoder are active at the same time, the input having the highest priority will take [[:wikt:precedence|precedence]]. It is an improvement on a simple encoder because it can handle all possible input combinations, but at the cost of extra logic.<ref>{{cite book |last1=Mano |first1=Moshe Morris |last2=Ciletti |first2=Michael D. |title=Digital Design |date=2007 |publisher=Pearson Prentice Hall |___location=Upper Saddle River, NJ |isbn=978-0-13-198924-5 |page=156 |edition=Fourth}}</ref>
Applications of priority encoders include their use in [[Programmable interrupt controller|interrupt controllers]] (to allow some [[interrupt request]]s to have higher priority than others), decimal or [[binary encoding]], and [[Analog-to-digital converter|analog-to-digital]] / [[Digital-to-analog converter|digital to-analog]] conversion.<ref>{{cite book |title=The TTL Applications Handbook |date=August 1973 |publisher=Fairchild Semiconductor |page=4-4}}</ref>
==Implementation==
A [[truth table]] of a single bit 4-to-2 priority encoder is shown, where the inputs are shown in decreasing order of priority left-to-right, and "x" indicates a [[don't care term]] - i.e. any input value there yields the same output since it is superseded by a higher-priority input. The (usually-included{{efn|For instance, the [[List of 7400-series integrated circuits|74x147]] 10-to-4 [[BCD (character encoding)|BCD]] priority encoder does not have a dedicated output valid signal. However, invalid is indicated by all outputs simultaneously high. https://www.ti.com/lit/ds/symlink/sn74ls148.pdf}}) "v" output indicates if the input is valid.
{| class="wikitable" style="margin:1em auto 1em auto; text-align:center;"
|+ 4 to 2 Priority Encoder
|- style="background:#def; font-weight:bold"
|-
|
|-
| {{no|0}} ||
|style="background: #FFC7C7; color: black; border-left:2px solid #000;"|0 || {{no|0}} || {{yes2|1}}
|-
|
|style="background: #FFC7C7; color: black; border-left:2px solid #000;"|0 || {{yes2|1}} || {{yes2|1}}
|-
| {{no|0}} || {{yes2|1}}
| 0 || 1 || x || x ||style="border-left:2px solid #000;"| 1 || 0 || 1▼
|colspan=2 {{n/a|x}}
▲
|-
| {{yes2|1}}
| 1 || x || x || x ||style="border-left:2px solid #000;"| 1 || 1 || 1▼
|colspan=3 {{n/a|x}}
▲
|}
[[File:A 4-2 Priority Encoder .jpg|alt=Gate-level diagram of a single bit 4-to-2 Priority Encoder|thumb|486x486px|[[Logic gate|Gate-level]] diagram of a single bit 4-to-2 priority encoder. I(3) has the highest priority.|center]]
Priority encoders can be easily connected in arrays to make larger encoders, such as one 16-to-4 encoder made from six 4-to-2 priority encoders - four 4-to-2 encoders having the signal source connected to their inputs, and the two remaining encoders take the output of the first four as input.The priority encoder is an improvement on a simple encoder circuit, in terms of handling all possible input [[Computer configuration|configurations]].▼
▲Priority encoders can be easily connected in arrays to make larger encoders, such as one 16-to-4 encoder made from six 4-to-2 priority encoders
== Recursive construction of priority encoders ==
Sources:<ref>{{Cite thesis|title=Architecture of block-RAM-based massively parallel memory structures : multi-ported memories and content-addressable memories|url=https://open.library.ubc.ca/cIRcle/collections/ubctheses/24/items/1.0314219|publisher=University of British Columbia|date=2016|first=Ameer M. S.|last=Abdelhadi}}</ref><ref>{{Cite book|last1=Abdelhadi|first1=Ameer M.S.|last2=Lemieux|first2=Guy G.F.|title=2015 IEEE 23rd Annual International Symposium on Field-Programmable Custom Computing Machines |chapter=Modular SRAM-Based Binary Content-Addressable Memories |date=May 2015|pages=207–214|doi=10.1109/FCCM.2015.69|isbn=978-1-4799-9969-9|s2cid=16985129 }}</ref><ref>{{Cite book|last1=Abdelhadi|first1=Ameer M. S.|last2=Lemieux|first2=Guy G. F.|title=2014 International Conference on Field-Programmable Technology (FPT) |chapter=Deep and narrow binary content-addressable memories using FPGA-based BRAMs |date=December 2014|pages=318–321|doi=10.1109/FPT.2014.7082808|isbn=978-1-4799-6245-7|s2cid=2074456 }}</ref>
A priority-encoder, also called leading zero detector (LZD) or leading zero counter (LZC), receives an <math>n</math>-bit input vector and detects the index of the first binary ‘1’ in the input vector. A valid signal indicates if any binary ‘1’ was detected in the input vector, hence the index is valid.
Priority-encoders can be efficiently constructed by recursion. The input vector is split into <math>k</math> equal fragments with <math>n/k</math> bits. A priority encoder <math>\textrm{PE}_{n/k}</math> with a narrower width of 𝑛/𝑘 is applied for each fragment. The valid bit of each of the <math>k</math> <math>\textrm{PE}_{n/k}</math>‘s goes to a <math>k</math> bit <math>\textrm{PE}_{n/k}</math> to detect the first valid fragment. The ___location of this fragment is the higher part of the overall index, and steers the exact ___location within the fragment itself to produce the lower part of the overall index.
The depth of the proposed structure is <math>\lceil\log_kn\rceil</math>, while the hardware area complexity is <math>\mathcal{O}(n)</math>. If Altera's Stratix V or equivalent device is used, <math>k=4</math> is recommended to achieve higher performance and area compression, since the mux can be implemented using 6-LUT, hence an entire ALM.
An open-source [[Verilog]] generator for the recursive priority-encoder is available online.<ref name=II2DCAM>{{Cite web|url=https://github.com/AmeerAbdelhadi/Indirectly-Indexed-2D-Binary-Content-Addressable-Memory-BCAM/blob/master/pe |first1=A.M.S. |last1=Abdelhadi |first2=G.G.F. |last2=Lemieux |title=Modular SRAM-based Indirectly-indexed 2D Binary Content Addressable Memory II2DCAM |publisher=The University of British Columbia |date=2014 }}<br/>
{{cite book |first1=A.M.S. |last1=Abdelhadi |first2=G.G.F. |last2=Lemieux |chapter=Modular SRAM-Based Binary Content-Addressable Memories |chapter-url=http://www.ece.ubc.ca/~lemieux/publications/abdelhadi-fccm2015.pdf |title=2015 IEEE 23rd Annual International Symposium on Field-Programmable Custom Computing Machines |publisher=IEEE |___location= |date=2015 |isbn=978-1-4799-9969-9 |pages=207–214 |doi=10.1109/FCCM.2015.69|s2cid=16985129 }}</ref>
[[File:PE-recursion.svg|alt=Priority-encoder (left) symbol (right) recursive definition.|center|thumb|416x416px|Priority-encoder (left) symbol (right) recursive definition.]]
A behavioral description of priority encoder in Verilog is as follows.<ref name=II2DCAM/> In this case, the LSB has the highest priority.<syntaxhighlight lang="verilog" line="1">
// behavioural description of priority enconder;
// https://github.com/AmeerAbdelhadi/Indirectly-Indexed-2D-Binary-Content-Addressable-Memory-BCAM
module pe_bhv
#( parameter OHW = 512 ) // encoder one-hot input width
( input clk , // clock for pipelined priority encoder
input rst , // registers reset for pipelined priority encoder
input [ OHW -1:0] oht , // one-hot input / [ OHW -1:0]
output reg [`log2(OHW)-1:0] bin , // first '1' index/ [`log2(OHW)-1:0]
output reg vld ); // binary is valid if one was found
// use while loop for non fixed loop length
// synthesizable well with Intel's QuartusII
always @(*) begin
bin = {`log2(OHW){1'b0}};
vld = oht[bin] ;
while ((!vld) && (bin!=(OHW-1))) begin
bin = bin + 1 ;
vld = oht[bin];
end
end
endmodule
</syntaxhighlight>
==Simple encoder==
[[File:A Simple 4-2 encoder using or gate.jpg|alt=A simple 4:2 Encoder using OR gate.|thumb|318x318px|A simple 4:2 Encoder using OR gate.]]
A simple encoder circuit is a [[one-hot]] to binary converter. That is, if there are 2<sup>''n''</sup> input lines, and at most only one of them will ever be high, the binary code of this 'hot' line is produced on the ''n''-bit output lines.▼
{{Main|Encoder (digital)}}
▲A [[Encoder (digital)|simple encoder]] circuit is a [[one-hot]] to binary converter. That is, if there are 2<sup>''n''</sup> input lines, and at most only one of them will ever be high, the binary code of this 'hot' line is produced on the ''n''-bit output lines.
▲!style="border-bottom:2px solid #000; border-left:2px solid #000;"| O<sub>1</sub>
==Notes==
{{Portal|Electronics}}
{{notelist}}
==References==
| |||