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[CS61C FA20] Lecture 14.3 - Intro to Synchronous Digital Systems: Signals and Waveforms — Transcript

by CS 61C Departmental · 2,782 words · 440 segments · language en · Watch on YouTube

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0:00and welcome back now let's learn about
0:03signals and waveforms
0:04how to think about how these values
0:06zeros and one might change over time
0:09oh my gosh time so let's start the
0:12beginning a clock is the heartbeat of
0:14the system
0:15our clock uh this particular signal
0:18is a beautiful if you've if you've seen
0:21um some of these terms before i hope
0:23you've seen these terms before
0:25you've got the idea of t which is the
0:27period
0:28which is the distance between a rising
0:30edge and the next rising edge that's
0:32important
0:34t and frequency are inversely related so
0:38frequency is the one over the period and
0:40period is one over the frequency okay
0:42and typically
0:43roughly these are in the the period is
0:46roughly one nanosecond
0:47and the frequency is roughly one
0:49gigahertz if the
0:50if the if the period goes
0:54to a third of a nanosecond that would
0:56mean the frequency is three gigahertz
0:58so think about that we've got voltage so
1:01this is our
1:02clock and it's going to vary between
1:04three volts and zero volts
1:05um and we're going to treat these as
1:07ones or zeros so so this is again
1:08abstractly thinking about these ideas
1:12signals are translated transferred over
1:16wires continuously and there's delays
1:18time takes time to go from here to there
1:20so we'll talk about that in a little bit
1:22we're going to treat them mostly as
1:24instantaneous because mostly we're not
1:26talking about a long transmission but as
1:28you
1:28actually get the distance between these
1:30signals to be great it ends up being um
1:32a real a real issue in fact grace mary
1:34hopper used to walk around with a piece
1:36of wire about this long and saying this
1:37is a nanosecond
1:38because it takes this long for a signal
1:40to start here and get
1:41to that distance if you work out the
1:42speed of light so
1:44that remember that um and also remember
1:46that a wire can only have one value at a
1:48time a single wire has one value at a
1:49time
1:50you have multiple wires optical things
1:52you can actually have multiples in a
1:53single optical channel you can have lots
1:54of signals but in a physical kind of
1:56copper wire
1:57you only have one signal at a time okay
2:00so here's an example of an outer circuit
2:03as we're going to start thinking about
2:04these block diagrams here's an adder
2:06look at this i've got n bits of b
2:11n bits of a and i have some number bits
2:14of this circuit now
2:15if i look at just let's look at b0 and
2:17b1
2:18there's some interesting things these
2:20things are going to change over time so
2:21this is voltage over time i'm looking
2:23here voltage
2:24as a function of time and i'm seeing
2:25that voltage you know here's my clock a
2:27nice very pretty clock nice square wave
2:29in the bottom
2:30but you're seeing there's some issues
2:32here this is not a perfect
2:33signal here this is not line up like
2:35here's my lineup it doesn't line up
2:37perfectly there's some issues here
2:38and it's also wiggling up here we're
2:40going to see that there's imperfections
2:41we're going to try to work around that
2:42with our signals as well so we saw that
2:45they're noisy
2:46they're not always perfectly flat and
2:49they don't line up
2:50there's a delay there's a delay in just
2:53the
2:53all the processing that has to be done
2:55in this circuit before the output
2:57um and maybe look at this this is delay
2:58on the input the delay of the input is
3:00not even coming in here who knows how
3:01long this
3:02this circuit delays and whether the
3:04output is even more more delayed if the
3:05output might even be more delayed
3:07how that is so we're going to have to
3:08deal with all those challenges between
3:10noise and delays
3:11this is real world folks this is a
3:13little harder so yes it's digital but
3:15there's some issues we should think
3:16about as we start to build our circuits
3:17together
3:18let's talk about some names so i have
3:21here's a nibble
3:22i've got here four parallel bits x0
3:25through x3
3:26okay and each of these were going to be
3:29nice for this
3:29picture with no delays each of these has
3:32a value when it's high
3:34we're going to call it a one when it's
3:36low we'll call it a zero
3:37so now you see this path this is kind of
3:39cool x0
3:40has different values hopefully
3:43synchronized with the clock
3:44one zero one one x one has
3:48zero one zero zero now here's the cool
3:51thing
3:51take your head and turn it sideways and
3:54what you see is i turn it sideways now
3:56i'm looking sideways at this number here
3:57we go
3:58now that's the higher order bit that's
4:00the msb
4:02or most significant bit and this is the
4:05lsb or least significant bit
4:07if you draw like that here's the lsb
4:10and here's the msb if you draw like that
4:13look
4:14i'm seeing 0 1 0 1. that's a 5.
4:18a 1 1 0 6 1 0 0 0
4:218 i've been i've memorized the whole
4:23i'll help you memorize that by the way
4:24zero zero zero one one and zero one one
4:26one seven so
4:28i can just think about this as
4:31a big capital x like a vector x
4:34which is really a vector and in some
4:36sense and capturing i draw it like this
4:38i don't like it this looks like i look
4:40like a chiclet i draw a little
4:42chick that's saying this has the value
4:43five and the value six and that saves me
4:45for him to draw
4:46four lines over time i just draw the
4:48value x and its number over time
4:50which really encodes the fact that
4:52they're really four bits doing the work
4:53but i'm going to draw it like this x to
4:55make it really very convenient okay so
4:57think about that
4:58to group this with that part of turning
4:59this is to group my four bits into
5:02one kind of four bit wide vector
5:06so now now i can think about that now
5:08here's a here we go an adder
5:10this is called a nibble adder look at
5:13that
5:14four bits of a come in four bits of b
5:16come in and a plus b
5:17is represented on the output c sometimes
5:20four bits can't be enough to do that
5:22that's when overflow would happen but
5:23let's for now let's pretend that
5:24overflow isn't happening
5:26and a and b are gonna be small enough
5:27there's no overflow so that's what we
5:28got this is fine
5:29so that's pretty cool so here's my a
5:32here's my a vector here's my b
5:34vector okay both nibbles and again this
5:36we just saw this last
5:38last slide a as we thought of as this
5:40four signals
5:41a zero small lower case a zero through a
5:43three
5:44and now i've got two and three and two
5:46three should add to five but what i'm
5:48noticing is there's something called
5:49a delay now i'm finally realizing that
5:51the fact that you know what this is real
5:52world there are delays it takes the time
5:54to do
5:54takes the time for some magical genie
5:57inside to do the work
5:58we're going to see what the magical
5:59genie is when we build it ourselves but
6:00did you do the work okay two plus three
6:02five okay it takes me some time take the
6:03genie some time to do that
6:04so there's going to be a delay between
6:06when
6:07for example here's a new three here's a
6:09new three here's a new 10.
6:12when does the output c say 13 well
6:15it still says 5 even though right a
6:17moment after this time
6:19i knew at that time that it was three
6:21and ten but it took some time there and
6:22we're going to call this the time
6:24between when
6:25the clock goes up really usually when
6:27the clock goes up till
6:28or when the inputs change i'll say
6:30inputs change until i see the output
6:33the correct value on the output we're
6:35going to call that
6:36the adder propagation delay and if this
6:38is an adder we call it out of
6:39propagation
6:40if this is a and it would call it the
6:42and propagation lays whatever
6:44the name of the block is propagation
6:46delay that says there's a delay between
6:48when the inputs are stable at the new
6:49values until when i can confidently say
6:51that the output has the correct value
6:53for whatever it's trying to calculate
6:55okay so new word here adder propagation
6:58delay
6:59pretty cool okay so let's keep playing
7:02with this
7:03as i start to have more and more complex
7:05signals
7:06systems i'm going to have a ton of
7:08signals and boy does it help to
7:10actually have a tool to look and see
7:13what's going high when what's going on
7:15oh look at this
7:16this they're never supposed to be this
7:19both one but look right for that little
7:20instant they're both one
7:21that can be a problem for myself for my
7:23system whatever it is so as i'm building
7:24these systems
7:25you need to have a piece of tool a
7:27debugger that will let you work with
7:30uh the signals in parallel see all the
7:31signals in parallel and be able to play
7:33with them in fact notice this
7:34this one look at this here they're
7:36thinking about this as values not as
7:38this here's the here's the
7:40here's the the vector sometimes you want
7:43to see the actual bits
7:44but you also want to see the vector so
7:45these these debuggers often let you
7:48cluster them or not cluster it's pretty
7:50cool okay that's kind of neat
7:53so big picture there are two kinds of
7:55circuits we're going to look at
7:56in the series of lectures and in really
7:58computer engineering we can categorize
7:59them to two ways
8:00kind number one is combinational logic
8:03circuits
8:03these if you took cs0 cs10
8:07these are just like pure functions just
8:10like pure functions this is also from
8:1161a
8:12it's a function that has no side effects
8:14no state it's memoryless
8:15the output is only a function of the
8:16input combinational logic circuits we
8:18love them very easy
8:20here's a set of inputs and here's an
8:21output there might be a delay in my
8:23combinational logic but
8:24there's no feedback there's no state
8:26it's just output is only a function of
8:28the inputs i'm ready to go
8:30and our adder was like that here's some
8:32bits and here's the output it's always
8:33going to be the same output for the same
8:35input that's the other critical piece of
8:36it
8:37or we also care about state elements and
8:40state elements are ones that
8:41have state they have memory boy if i
8:43didn't have memory my computer won't be
8:45able to store the data that i've created
8:46so
8:47we need state elements to store our data
8:49registers
8:50caches caches memory disk all these
8:52things have state they remember
8:54what you put them there and i have
8:56combination of logic to do some
8:57calculations
8:58and so we're going to have two of those
8:59kinds of circuits and
9:01we need both of them in what we're going
9:02to be building okay so combinational
9:04logic circuits are cl
9:05and state elements here's a circuit with
9:08state
9:09and i haven't told you how it works but
9:10i'm going to talk about what it is
9:12this is called a register
9:16you've seen a register when we were
9:16talking about risk five but here is an
9:18example register is
9:19it has n bits of input and bits of
9:23output
9:23and it has a loader and this little
9:26circuit says that something magical
9:27happens when
9:28that circuit goes high so when that goes
9:31high
9:31here's what the register does i'm a
9:33register i'm sitting here i've got my
9:35outputs it's all
9:36my output is whatever i've been stored
9:38with i have some value stored here
9:39here's my output
9:40okay here we go load goes high
9:44i turn around i grab the value
9:47of input and i hold it i remember it and
9:50now i'm loading it i'm loading this into
9:52myself
9:53and now i ignore it once that goes high
9:55i turn on quickly grab it and then turn
9:56around
9:57and i hold that that's what i hold you
9:59gave me five okay here's
10:00five holding five oh now it's changing
10:03to 10 20. i don't care i don't care what
10:04my input says because
10:06because load is still low ready rising
10:08edge of load now it's a 7
10:10turn around grab the 7 and 7.
10:13that's it i'm holding 7. now it's
10:15changing load is still low
10:16input is changing i don't care i'm
10:18holding it stable state
10:20i'm holding the seven that's the idea
10:23what often we do is we clock these
10:26devices
10:27so now rather than load going up every
10:29once in a while
10:30i'm going to go up every single clock
10:32cycle i'm here i got my seven and then
10:35clock goes up turn around grab
10:36whatever's there
10:38now it's a 12. here's my i should have
10:41said 12.
10:42here's my 2. i don't know what 12 feet
10:442.
10:46okay clock goes up again whatever it
10:48happens to be
10:49so there's a rhythmic nature to it okay
10:51and so normally we
10:53um normally we're going to clock these
10:55devices and having them clocked is
10:57is great because now there's a rhythm
10:59and now data's kind of moving in chunks
11:01like an assembly line
11:04they move to the next stage everything
11:06just kind of moves to the right and data
11:07so that's going to be great as we build
11:09circuits we have our data kind of
11:11chunk to the right that's exactly what
11:12we'll use this register that's going to
11:14be clocked so we typically clock our
11:16registers not always
11:17but we often we often do
11:20in conclusion clocks are the heartbeat
11:23the pulse of our circuits
11:25voltages are analog voltages are who
11:28knows what they are but i'm going to
11:29quantize them
11:30it's zero to three volts next year it's
11:31zero and 2.5 volts whatever they build
11:33but i'm going to quantize them to be a
11:35zero and one and think of them in a kind
11:36of
11:36soft abstract abstract way as a zero to
11:39one from now on
11:40circuit delays are a fact of life we saw
11:42that everything there's real world
11:44natures
11:45the there's not just delays but the
11:47values are often fuzzy
11:49and one of the things we're going to do
11:50from our from our circuits is if the
11:51value came in fuzzy like let's say it's
11:53a little bit below one it's still a one
11:54but it's like
11:54not three volts it's 2.5 we're gonna
11:57make sure that
11:58that circuit cleans it up if every
12:00circuit cleans it up
12:01so that input was coming in was a little
12:03below two below three
12:05output is gonna be solid three and the
12:06only way that they're gonna have noise
12:09the only reason it would not be three is
12:10then noise or maybe maybe there's some
12:12resistance on the line so i had to go
12:13from here to here and it started a three
12:15and it was lower by the time it got
12:16there so the real world is going to
12:18influence this by adding noise to our
12:20system or having
12:21you know having a distance with
12:22resistance across the line but every one
12:24of our core blocks is going to try to
12:26clean the circuit up if it came off a
12:27little bit higher than zero
12:29we're going to clamp it down to zero if
12:30it came in a little bit lower than the
12:32three a little above three we're gonna
12:33try to make a clamp but at three so our
12:35job of each of these blocks is going to
12:36be clean the signal up
12:37and then who knows in the in the trans
12:39in the transmission of that data to the
12:41next block
12:42maybe your voltage got up maybe some
12:43noise from the connection guy maybe
12:44there's a distance of resistance
12:46whatever it is
12:47that might be not perfect zero and one
12:50coming in but we're going to try to
12:50clean up to be a zero and one coming out
12:52that's the idea of our blocks
12:54and in summary there's two kinds of
12:55circuits combinational logic or cl
12:57and state circuits like registers we're
13:00going to learn more about those and even
13:01how to build a register in the next
13:02series of lectures we'll see you there

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