4.2 Digital Logic, DIO
and DAC
• why digital logic?
• truth tables for digital logic
P NOT
P AND
P OR
P XOR
P NAND
P NOR
• examples of logic circuits
• digital input and output (DIO)
• digital-to-analog conversion (DAC)
4.2 : 1/11
Why Digital Logic?
• High-voltage instruments are often interlocked to protect the
user. Each access point is connected to a switch that has a binary
output (0 closed, 1 open). The high voltage is shut down if any
access point is opened. This is accomplished with OR logic.
shut_off? = sw1 OR sw2 OR sw3 OR sw4
• Before a spectrum is recorded it might be necessary for the user
to click on a scan button, the monochromator be set to the
starting wavelength, and the sample chamber door be shut.
record? = scan AND startλ AND door_shut
• These types of logic decisions can be made in hardware or
software. The hardware option simplifies the computer program
and reduces the number of bits of logic information that need to
be input to the computer.
4.2 : 2/11
Logic Gates and Truth Tables (1)
• For electronics a 1 is taken as true and a 0 as false. The most
common logic family is transistor-transistor logic (TTL) where
+5 V = 1 and 0 V = 0.
• NOT gate: Q = NOT A
also written as _____
A
0
1
Q
1
0
A
• AND gate: Q = A AND B
A
0
0
1
1
4.2 : 3/11
B
0
1
0
1
Q
0
0
0
1
Q
also written as _____
A
B
Q
Logic Gates and Truth Tables (2)
• OR gate: Q = A OR B
A
0
0
1
1
B
0
1
0
1
also written as _____
Q
0
1
1
1
• XOR gate: Q = A XOR B
A
0
0
1
1
B
0
1
0
1
Q
0
1
1
0
A
Q
B
also written as ______
A
B
Q
• note that OR and XOR differ when both inputs are 1
4.2 : 4/11
Logic Gates and Truth Tables (3)
• NAND gate: Q = A NAND B
A
0
0
1
1
B
0
1
0
1
Q
1
1
1
0
• NOR gate: Q = A NOR B
A
B
Q
0
0
1
0
1
0
1
0
0
1
1
0
4.2 : 5/11
also written as ________
A
B
Q
also written as ________
A
B
Q
Example Logic Circuit (1)
use OR, NAND and AND logic to create XOR logic
(
A ⊕ B= ( A+B )i AiB
A
0
0
1
1
B
0
1
0
1
(OR)
0
1
1
1
(NAND)
1
1
1
0
)
()AND()
A
B
Q
A
B
4.2 : 6/11
Example Logic Circuit (2)
• use XOR, AND and OR logic to create an adder with carry from
the right and carry to the left: A + B + Cin = S + Cout
• the required truth table is given below (rotated 90°)
A
Cin
A
B
S
Cout
0 0 0 0 1 1 1 1
0 0 1 1 0 0 1 1
0 1 0 1 0 1 0 1
0 1 1 0 1 0 0 1
____________________
B
Cin
Cin
A
B
• to see this circuit in action see: www.play-hookey.com
4.2 : 7/11
S
Cout
Digital Input & Output (DIO)
• binary output generated by external
digital logic often needs to be
communicated to a computer
program
• similarly, a logic calculation
performed by software often needs to
be communicated to an external
circuit
• the number of bits available for DIO
depends upon the specific product
with multiples of 8 being common
• for output the computer sets the
bits and the register holds the values
until they are read by the external
circuit
• for input the external circuit sets
the bits and the register holds the
values until they are read by the
computer program
4.2 : 8/11
0V
0
+5 V
1
digital
control
logic
+5 V
1
0
0V
0
0V
0
0V
0
0V
0
0V
experiment/
instrument
DIO Continued
• besides the DIO registers, ___________ (flags) are necessary
• For example, an "input ready" bit tells the computer that a
new value is ready for reading. After the computer reads the
DIO it might set an "input read" bit that tells the external circuit
that it can provide updated information. This is called
handshaking.
• A external circuit can "watch" an "output ready" control bit.
With this approach the logic output will not be read until the
computer has updated the DIO.
• if the experiment has voltages that might inadvertently
damage the DIO circuitry (or worse get into the computer), the
outputs can be __________________ using light emitting
diode/photodiode combinations
• when the external circuit uses high voltage or the instrument
is in a corrosive environment, _______________ can transfer
the digital logic information
4.2 : 9/11
Digital-to-Analog Conversion
• Often a digital value generated by a program needs to be
converted into an external voltage. An example might be the
generation of a _________________ in electrochemistry.
• In the DAC shown below individual bits control a transistor
switch that provides current to the op-amp. The resistor ladder
makes the current associated with each bit to be exactly 1/2 that
of the bit to the left. The current from all bits is summed. The
op-amp behaves as a ______________________________.
50 k
50 k
50 k
100 k
+10 V
0
0
1
1
50 k
!
100.0 μA
MSB
4.2 : 10/11
50.0 μA
25.0 μA
12.5 μA
LSB
+
0 to -9.375 V
DAC Performance
• when all the binary
combinations are output in
order, the DAC output
resembles a __________
• commercial DACs have from
4 to 18 bits
(16 to 262,144 steps)
• common output ranges
might be 0 to 10 V or
-5 to +5 V
• some DACs have software
controlled voltage ranges
• most DACs can output new
voltages every ___________
permitting the generation of
arbitrarily-shaped waveforms
4.2 : 11/11
-10.000 V
-7.500 V
-5.000 V
-2.500 V
LSB = -0.625 V
-0.000 V
Binary Input