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Transcript of EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite...
![Page 1: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/1.jpg)
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EECS 370 Discussion
xkcd.com
![Page 2: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/2.jpg)
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EECS 370 Discussion
Topics Today:– Floating Point
– Finite State Machines
– Combinational Logic
– Sequential Logic
![Page 3: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/3.jpg)
EECS 370 Discussion
Floating Point
ExponentBiased by 127
SignificandAdditional 1 before the decimal sign
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EECS 370 Discussion
Floating Point
Don’t forget about zero!
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![Page 5: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/5.jpg)
EECS 370 Discussion
Floating Point
Addition-1.1011*(22) + 1.01*(20)
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EECS 370 Discussion
Floating Point
Addition-1.1011*(22) + 1.01*(20)
= -1.0110*(22)
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![Page 7: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/7.jpg)
EECS 370 Discussion
Floating Point
Addition-1.1011*(22) + 1.01*(20)
[-6.75] [1.25]
= -1.0110*(22) [-5.5]
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![Page 8: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/8.jpg)
EECS 370 Discussion
Floating Point
Multiplication-1.1011*(22) * 1.01*(20)
[-6.75] [1.25]
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![Page 9: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/9.jpg)
EECS 370 Discussion
Floating Point
Multiplication-1.1011*(22) * 1.01*(20)
[-6.75] [1.25]
= -1.0000111*(23)
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![Page 10: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/10.jpg)
EECS 370 Discussion
Floating Point
Multiplication-1.1011*(22) * 1.01*(20)
[-6.75] [1.25]
= -1.0000111*(23) [-8.4375]
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![Page 11: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/11.jpg)
EECS 370 Discussion
Finite State Machines
Diagram of State, Conditions to change state, and OutputsConditions to change are based on inputs
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EECS 370 Discussion
Finite State Machines
Example: Output a 1 on the pattern 001
States:Pattern ‘1’Pattern ‘0’Pattern ‘00’Pattern ‘001’ => Output = 1
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![Page 13: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/13.jpg)
EECS 370 Discussion
Combinational Logic
Digital circuit representing a Boolean equation
Truth tables!!
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EECS 370 Discussion
Combinational Logic
More Complex Circuits: Mux Decoder
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A
S
BC Out1
Out2
A0A1
Out3
Out0
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EECS 370 Discussion
Combinational Logic More Complex Circuits: Full Adder
Half Adder
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EECS 370 Discussion
Combinational Logic More Complex Circuits: Ripple Carry Adder
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EECS 370 Discussion
Combinational Logic Propagation Delay
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EECS 370 Discussion
Combinational Logic Propagation Delay
Slows down the speed of your circuit!
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EECS 370 Discussion
Combinational Logic Most Complex Circuits: Carry Look-ahead Adder
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EECS 370 Discussion
Sequential Logic Combinational Logic
StatelessOutput is direct function of current input
Sequential LogicStatefulOutput is function of current input and past inputClocked!
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EECS 370 Discussion
Sequential LogicLatches SR Latch D Latch
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EECS 370 Discussion
Sequential LogicFlip Flops Positive Edge Triggered
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EECS 370 Discussion
Sequential Logic
Why do we want clocked logic?Specifies a time by which all operations are “done”Results before that time do not matter
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Delays in combinational circuits are very real.
Here’s an example with a ripple carry adder.
AN EXAMPLE OF WHY THIS MATTERS
![Page 25: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/25.jpg)
Let’s zoom in on the interesting part.
AN EXAMPLE OF WHY THIS MATTERS
The value of a goes from 7 to 1 here
![Page 26: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/26.jpg)
Let’s zoom in on the interesting part.
AN EXAMPLE OF WHY THIS MATTERS
There’s propagation delay before the adder even starts to change values.
![Page 27: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/27.jpg)
Let’s zoom in on the interesting part.
AN EXAMPLE OF WHY THIS MATTERS
The value stabilizes
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Let’s zoom in on the interesting part.
AN EXAMPLE OF WHY THIS MATTERS
The next clock edge comes along
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Let’s zoom in on the interesting part.
AN EXAMPLE OF WHY THIS MATTERS
The latch opens up (and shows new value)
The flip-flop grabs new value.
![Page 30: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/30.jpg)
Let’s zoom in on the interesting part.
AN EXAMPLE OF WHY THIS MATTERS
B changes now,while the clock is still high.
![Page 31: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/31.jpg)
Let’s zoom in on the interesting part.
AN EXAMPLE OF WHY THIS MATTERS
Again, there’s propagation delay before the adder starts to change.
![Page 32: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/32.jpg)
Let’s zoom in on the interesting part.
AN EXAMPLE OF WHY THIS MATTERS
The value in the latch changes too!
![Page 33: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/33.jpg)
Let’s zoom in on the interesting part.
AN EXAMPLE OF WHY THIS MATTERS
The next falling edge comes along
![Page 34: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/34.jpg)
Let’s zoom in on the interesting part.
AN EXAMPLE OF WHY THIS MATTERS
The adder stabilizes.
![Page 35: EECS 370 Discussion 1 xkcd.com. EECS 370 Discussion Topics Today: – Floating Point – Finite State Machines – Combinational Logic – Sequential Logic 2.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e1f5503460f94b0ad28/html5/thumbnails/35.jpg)
Let’s zoom in on the interesting part.
AN EXAMPLE OF WHY THIS MATTERS
The latch locked with the wrong value!