Announcementsmid-term on Thursday12:30 – be on time.Calculators allowed (required!)

No assignment due this week Assignment 6 posted on ThursdayProject 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 11 01 1

A B D E C0 0 0 1 0

0 1 1 1 11 0 1 1 11 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