announcements mid-term on thursday 12:30 – be on time. calculators allowed (required!) no...
TRANSCRIPT
Announcements
mid-term on Thursday
12:30 – be on time.
Calculators allowed (required!)
No assignment due this week
Assignment 6 posted on Thursday
Project ideas to me by Nov 1st
Lecture 15 Overview
• Digitization
• Logic families
• Logic and Gates
A jump ahead - Lab Information: The Data Flipflop
A signal on the D INPUT is transferred to the Q OUTPUT during the positive going transition of the clock pulse. CLEAR and PRESET are independent of the clock and accomplished by a low on the appropriate input.
http://fac-web.spsu.edu/cs/faculty/bbrown/web_lectures/sequential/
Digitization
• How do we convert a time varying signal into digital bits?
• Sampling rate and resolution.
Digitizing a signal•
0
Digitizing a signal•
Digitizing a signal
Camera
1.8 m
•499 PMTs
•Photonis XP2970
•0.15º spacing
Data Acquisition • PMT signals digitised with
500MHz sampling FADCs• Data rates
– 24 samples/channel– 13.5 kb/event @ 100 Hz– 5 Gb/hour
Integrated Pulse
Cosmic Ray showers measured by VERITAS
(each frame 2 ns long)
Logic Gates
How do you process a digital signal?
Logic Families: TTL
• TTL = transistor-transistor logic• TTL output: LOW<0.4V, HIGH>2.4V• TTL input: LOW < 0.8V, HIGH > 2.0V• Based on BJTs• Supply voltage = 5V
2.4V
0.4V
CMOS• CMOS logic = Complementary MOS• Based on MOSFETs • CMOS levels depend upon the supply voltage and provide larger noise margins than TTL • Many other logic families and subtle variations exist - NIM, ECL, LVDS etc. • Generally simple to connect devices from the same logic families together - interfacing different families is more complex (See Horowitz and Hill Ch 9.01)
How do you process a digital signal?
• Have only two states– 1,0 map naturally to logic states True/False– Use Boolean algebra– Carry out calculations using a "truth table": list all possible
combinations of inputs and corresponding output e.g.
• A, B and C are digital signals• n inputs give 2n combinations
Each logic function can be performed with logic gate circuit.
Digital logic designers do not need to care about what is inside a gate
Today's microprocessors can contain >100 million logic gates
The AND gate
• The output of an AND gate is TRUE if, and only if, both inputs are TRUE• The symbol for an AND operation is the multiplication symbol "∙"• This is often omitted, so "A AND B" is written "AB"• Note that the truth table looks correct for the multiplication of A and B
The NOT gate
• Also known as an inverter• Symbol is the overbar ¯. An apostrophe ' is also used (e.g. A')• There are several realizations of a NOT gate possible
1) This is the usual schematic symbol2) Sometimes it is shown explicitly as a gate3) Tying the inputs of a NAND gate together yields a NOT4) Tying the inputs of a NOR gate also yields a NOT
The NAND gate
• Note the connection between NAND and AND. The output of a NAND gate is the opposite of AND (NAND=NOT AND).
• Note the symbol for the NAND operation (AND, NOTed). Schematically, the small circle at the output end of the AND symbol means NOT
• NAND is one of the most heavily used binary operations
The OR gate
• The output is TRUE if any of the inputs are TRUE• Symbol is +
The NOR gate
• The output is TRUE only if all of the inputs are FALSE• Inverse of OR
Gate Combination
Which of the following inputs gives D=1 ?
• Answer: a and c
Gate Combinations
• What is the truth table for this circuit?• The effect of this circuit is the same
as an XOR gate.
A B D E C0 0
0 1
1 0
1 1
A B D E C0 0 0 1 0
0 1 1 1 1
1 0 1 1 1
1 1 1 0 0
The XOR gate
• Exclusive OR• The output is TRUE only if one or the other, but not both, inputs are TRUE• Symbol is
• The XOR gate can be used as an "optional inverter"• e.g. to invert or not invert an input signal at B, based on a controlling input
at A
C
C=A XOR BC=AB
A B C(in) (in) (out)
0 0 0
0 1 1
1 0 1
1 1 0
The XNOR gate
• Inverse of XOR• The output is TRUE only if both inputs are the same.• "logical equality"
C
C=A NOR BC=AB
A B C(in) (in) (out)
0 0 1
0 1 0
1 0 0
1 1 1