SLIDE 1
https://images-na.ssl-images-amazon.com/images/I/A1w4iP5ov-L._SY879_.jpg
Translate this table to a circuit
Full name
- Th. 9/20
input
- utput
x y a b c d
1 1 1 1 1 1 1 1
fill me in!
- - PDF document
- - PDF document
https://images-na.ssl-images-amazon.com/images/I/A1w4iP5ov-L._SY879_.jpg Translate this table to a circuit input output fill me in! x y a b c d 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 Full name Th. 9/20
SLIDE 2
SLIDE 3
Translate this table to a circuit
Full name
- Th. 9/20
input
- utput
x y a b c d
1 1 1 1 1 1 1 1
2-bit decoder
SLIDE 4
Levels of abstraction
Stored-program computers Random-access memory (RAM) Registers 1-bit memory: latches Logic gates Transistors / switches today next week twoday (s ago)
SLIDE 5
What kinds of problems can computers solve?
Decision problems on finite, bitstring inputs.
What counts as a problem? What counts as a computer?
Can combinational logic solve all the problems that a DFA can? How about a Turing Machine?
SLIDE 6
Can we do this?
If we can’t, then boolean functions aren’t as powerful as DFAs.
𝚻 = {0}
SLIDE 7
Use minterm expansion!
(1) Write down the truth table for this DFA. The output of the function should be a 1 if it accepts; 0 if it rejects. (2) Use minterm expansion to create the circuit from the table.
Impossible task!
we cannot build a circuit for this DFA
SLIDE 8
Hint: 0 gates
Pass-through
input
- utput
time t0 t1 t2 t3 t4 t5 t6 t7
I’m (not) pressing the button right now.
SLIDE 9
Phase behavior: set
set
- utput
time t0 t1 t2 t3 t4 t5 t6 t7
I (haven’t yet) pressed the button. (toggle on) Hint: 1 gate Hint: Either I’m pressing the button now. OR The output was 1 at some point.
SLIDE 10
Phase behavior: set / reset
reset set
- utput
time t0 t1 t2 t3 t4 t5 t6 t7
I can toggle the button on and off. Hint: 3 gates Hint: OR, AND, NOT S/R latch
SLIDE 11
Pass-through via set / reset
data
- utput
time t0 t1 t2 t3 t4 t5 t6 t7
I’m (not) pressing the button right now.
S/R latch
SLIDE 12
input
- utput
strobe data set reset
1 1 1 1 1 1
Hint:
Pass-through or set / reset
strobe data
- utput
time t0 t1 t2 t3 t4 t5 t6 t7
I can toggle between pass-through and remembering the state from a moment in time. D latch
S/R latch
SLIDE 13
https://images-na.ssl-images-amazon.com/images/I/61wzOqnANGL._SX679_.jpg
SLIDE 14
A 512K x 8 RAM (About 4.2 million bits)
Random-access memory (RAM)
SLIDE 15
Interface: we can read or write one of four rows of memory, and each row stores three bits
A small piece of RAM
SLIDE 16
Implementation
A small piece of RAM
SLIDE 17
Addressing: select which “line”
A small piece of RAM
SLIDE 18
Write mode
A small piece of RAM
SLIDE 19
A small piece of RAM
SLIDE 20
Wire data bits to corresponding memory bits
A small piece of RAM
SLIDE 21
Wire data bits to corresponding memory bits
A small piece of RAM
SLIDE 22
Wire data bits to corresponding memory bits
A small piece of RAM
SLIDE 23
What kinds of problems can computers solve?
Decision problems on finite, bitstring inputs.
What counts as a problem? What counts as a computer?
Can sequential logic solve all the problems that a DFA can? How about a Turing Machine?