{"id":118,"date":"2016-07-05T13:03:03","date_gmt":"2016-07-05T12:03:03","guid":{"rendered":"https:\/\/blogs.ncl.ac.uk\/jrbeaumont\/?p=118"},"modified":"2016-07-05T13:03:03","modified_gmt":"2016-07-05T12:03:03","slug":"concepts-v-set-reset-latch","status":"publish","type":"post","link":"https:\/\/blogs.ncl.ac.uk\/jrbeaumont\/2016\/07\/05\/concepts-v-set-reset-latch\/","title":{"rendered":"Concepts V: Set-Reset Latch"},"content":{"rendered":"

Set-Reset Latch<\/strong><\/span><\/p>\n

After learning how a C-element<\/a> can be produce with concepts, we can introduce other gates. In this case another fairly standard gate, a latch<\/em>.<\/p>\n

The operation of a latch is to hold a given value. There are several different types of latch, but in this case we will talk about a\u00a0Set-Reset latch (SR Latch).\u00a0<\/em>This latch has two inputs, one will\u00a0set<\/em> the latch when high, causing its one output to be high. The second input will\u00a0reset<\/em> the latch when it is high, causing its output to be low.<\/p>\n

So lets see how we can specify this using concepts.<\/p>\n

Concepts<\/span><\/strong><\/p>\n

For this, let’s start off by referring to the two inputs as\u00a0a\u00a0<\/strong>and\u00a0b<\/strong>. The output is\u00a0c<\/strong>.<\/p>\n

So, first of all, lets think about how we can set the latch:<\/p>\n

set = a+\u00a0\u21dd c+\u00a0\u22c4 a-\u00a0\u21dd c-<\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/p>\n

And it’s that simple. Simply put, when one of the outputs,\u00a0a<\/strong> in this case, goes high, we want the output,\u00a0c<\/strong>, to go high.<\/p>\n

So we have described the interaction for set using one of the inputs and the output, now lets describe the reset action:<\/p>\n

reset = b+<\/strong>\u00a0\u21dd c-\u00a0\u22c4 b-\u00a0\u21dd c+<\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/p>\n

This will cause the output to go low when the\u00a0second input,\u00a0b<\/strong>, goes high.<\/p>\n

These two concepts describe the operation of a SR-latch. But we still need to think about how the SR-latch will act initially, such as when it first receives power.<\/p>\n

Unless specifically required, we should assume that the output of the latch should be low at startup. Because of this, we don’t want it to be set initially by\u00a0a<\/strong> being high, so we can set this to 0 initially also.<\/p>\n

However, with the second input,\u00a0b<\/strong>, setting this high at this point would\u00a0ensure that the output will reset to 0 at start up, but if the initial state of\u00a0c<\/strong> is already set to low initially, we shouldn’t need to set\u00a0b\u00a0<\/strong>to high, so we will set the initial state of this to low too.<\/p>\n

The initial state concept<\/a> will be as follows:<\/p>\n

initialState = initialise(a, 0)\u00a0\u22c4 initialise(b, 0)\u00a0\u22c4 initialise(c, 0)<\/strong><\/strong><\/strong><\/p>\n

Now let’s create the scenario concept for the SR-Latch:<\/p>\n

SRLatch = set\u00a0\u22c4 reset\u00a0\u22c4 initialState<\/strong><\/strong><\/strong><\/p>\n

And this can be converted to a Signal Transition Graph, so this specification\u00a0can be verified, simulated, tested and then synthesised. The STG for a SRLatch will be as follows:<\/p>\n

\"STG_SR_Latch\"<\/a><\/p>\n

This is a fairly simple STG, but simulation would prove that setting\u00a0a\u00a0<\/strong>high will allow\u00a0c<\/strong> to transition high. Once it has transitioned high, it cannot transition low until\u00a0b<\/strong> has been set high.<\/p>\n

For some simpler understanding of how this latch works, we can change some of the signal names.\u00a0In this case, we will change\u00a0a<\/strong> to\u00a0s<\/strong>, which stands for\u00a0set.\u00a0<\/strong><\/em>b\u00a0<\/strong>will be set to\u00a0r<\/strong>, which stands for reset. Finally, we can call\u00a0c<\/strong>,\u00a0q.\u00a0<\/strong>q<\/strong> is a standard output symbol for latches.<\/p>\n

This will change the concepts to the following:<\/p>\n

set = s+\u00a0\u21dd q+\u00a0\u22c4\u00a0<\/strong><\/strong><\/strong><\/strong>s-\u00a0\u21dd q-<\/strong><\/strong>
\nreset = r+<\/strong>\u00a0\u21dd q-\u00a0\u22c4\u00a0r-<\/strong>\u00a0\u21dd q+<\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong>
\ninitialState = initialise(s, 0)\u00a0\u22c4 initialise(r, 0)\u00a0\u22c4 initialise(q, 0)<\/strong><\/strong><\/strong>
\nSRLatch = set\u00a0\u22c4 reset\u00a0\u22c4 initialState<\/strong><\/strong><\/strong>
\n<\/strong><\/strong><\/p>\n

This will produce the following STG:\"STG_SR_Lath2\"<\/a><\/p>\n

Changing the names of the signals does not affect the operation.<\/p>\n

Now the SR-Latch has been defined, if a user has signals which will be inputs to a latch, they can use the concept and pass their signals into this, in the order of\u00a0s, r\u00a0<\/strong>and\u00a0q<\/strong>. \u00a0For example someone can use the concept:<\/p>\n

SRLatch(x, y, z)<\/strong><\/p>\n

In this case, x<\/strong> will be the set signal,\u00a0y<\/strong> is the reset and\u00a0z<\/strong> will be the output.<\/p>\n

Some reuse<\/span><\/strong><\/p>\n

As is usually the case with concepts, we can define a SR-Latch using previously defined gates as concepts.<\/p>\n

First of all, if we look at\u00a0the\u00a0set\u00a0<\/strong>concept, it is clear that\u00a0s\u00a0<\/strong>and\u00a0q\u00a0<\/strong>form a buffer<\/a>. So this can be rewritten as:<\/p>\n

set = buffer(s, q)<\/strong><\/p>\n

The\u00a0reset<\/strong> concept can also be redefined. In this case, it acts as an inverter<\/a>:<\/p>\n

reset = inverter(r, q)<\/strong><\/p>\n

As the initial state doesn’t need to be changed, we can compose these concepts as above to produce the SRLatch concept:<\/p>\n

SRLatch = set\u00a0\u22c4 reset\u00a0\u22c4 initialState<\/strong><\/strong><\/strong><\/strong><\/strong><\/p>\n

Or we can reduce the number of concepts defined and compose these as follows:<\/p>\n

SRLatch = buffer(s, q)\u00a0\u22c4 inverter(r, q)\u00a0\u22c4 initialState<\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/p>\n

There are of course several ways of specifying an SRLatch using concepts, but these are two of the simpler ways, either using signal-level concepts, or predefined gate-level concepts. The preference is entirely on the user.<\/p>\n

Finally<\/strong><\/span><\/p>\n

In this post, we have explained another simple logic gate. The discussion includes the basic operation being specified as signal-level concepts, or by taking this a step higher and using pre-defined gates.<\/p>\n

We have also shown how while the concept defines certain signal names, these aren’t set. A default SRLatch concept will use these signal names, but if these signals are not used in a design, a user can pass the desired signal names into the concept, and these names will replace the default ones.<\/p>\n

This blog series will continue soon, with the inclusion of further logic gates and how they can be defined simply.<\/p>\n","protected":false},"excerpt":{"rendered":"

Set-Reset Latch After learning how a C-element can be produce with concepts, we can introduce other gates. In this case another fairly standard gate, a latch. The operation of a latch is to hold a given value. There are several different types of latch, but in this case we will talk about a\u00a0Set-Reset latch (SR … Continue reading Concepts V: Set-Reset Latch<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":6010,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,5,2,7,10,6,1],"tags":[],"class_list":["post-118","post","type-post","status-publish","format-standard","hentry","category-asynchronous","category-buffer","category-concepts","category-inverter","category-latch","category-logic-gate","category-uncategorised"],"_links":{"self":[{"href":"https:\/\/blogs.ncl.ac.uk\/jrbeaumont\/wp-json\/wp\/v2\/posts\/118","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ncl.ac.uk\/jrbeaumont\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ncl.ac.uk\/jrbeaumont\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ncl.ac.uk\/jrbeaumont\/wp-json\/wp\/v2\/users\/6010"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ncl.ac.uk\/jrbeaumont\/wp-json\/wp\/v2\/comments?post=118"}],"version-history":[{"count":8,"href":"https:\/\/blogs.ncl.ac.uk\/jrbeaumont\/wp-json\/wp\/v2\/posts\/118\/revisions"}],"predecessor-version":[{"id":134,"href":"https:\/\/blogs.ncl.ac.uk\/jrbeaumont\/wp-json\/wp\/v2\/posts\/118\/revisions\/134"}],"wp:attachment":[{"href":"https:\/\/blogs.ncl.ac.uk\/jrbeaumont\/wp-json\/wp\/v2\/media?parent=118"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ncl.ac.uk\/jrbeaumont\/wp-json\/wp\/v2\/categories?post=118"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ncl.ac.uk\/jrbeaumont\/wp-json\/wp\/v2\/tags?post=118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}