Digital Techniques 1 for Robotics ELEX 1215

Upon successful completion, the student will be able to:

BINARY NUMBER SYSTEM

• Perform number system conversions between binary and decimal numbers.
• Describe differences between analog and digital.
• Describe fundamental theory of number systems.
• Convert between binary and decimal numbers.

SWITCHES AND LOGIC SOURCES

• Design logic sources for use with electronic logic.
• Describe SPST, SPDT, DPST, and DPDT switches.
• Identify switch types (push button, slide, toggle, DIP, rotary).
• Define a convention for switch handles and contacts.
• Use an ohmmeter to evaluate switch contact configurations.
• Demonstrate the need for electronic logic and the required voltage level inputs.
• Define logic levels.
• Generate a logic variable using a single throw switch and a pullup (or pulldown) resistor.
• Generate a logic variable and its complement using a double throw switch and two pullup (or pulldown) resistors.
• Build, test, measure and troubleshoot logic sources.

BOOLEAN EQUATIONS AND TRUTH TABLES

• Use AND, OR, and NOT in Boolean equations.
• Define AND, OR, and NOT as logical operators.
• Define Boolean equations, operators and precedence of operation.
• Use one (1) to represent TRUE and zero (0) to represent FALSE.
• Derive Boolean expressions from English language statements.
• Define and construct truth tables using the binary number system
• Generate truth tables from Boolean equations.

LOGIC SYMBOLS FOR AND, OR, INVERTER

• Use AND, OR, and INVERTER symbols to represent logic circuits.
• Define the AND, OR, and INVERTER logic symbols and the corresponding truth tables.
• Generate logic symbol diagrams from Boolean equations.
• Generate Boolean equations from logic symbol diagrams.
• Generate truth tables from logic symbol diagrams.

ELECTRONIC LOGIC GATES

• Design circuits using logic symbols. Use NAND and NOR gates to implement logic circuits.
• Define the NAND and NOR electronic logic gates.
• Develop the Boolean equations and the truth tables for the NAND and NOR gates.
• Define the input characteristics of electronic gates.
• Define the output characteristics (sink, source) of the electronic gates.
• Define allowable voltage ranges for inputs and outputs of CMOS gates.
• Analyze the effects of open inputs for CMOS gates.
• Analyze loading and fanout capabilities of CMOS gates.
• Calculate noise margins and power dissipation for CMOS gates.
• Interface LEDs to electronic gates.

DESIGN WITH LOGIC GATES

• Develop the alternate symbols for logic gates.
• Follow “bubble-to-bubble” rules to draw logic diagrams.
• Develop Boolean equations from logic diagrams.
• Define Sum of Products and Product of Sums forms of Boolean expressions.
• Design circuit diagrams using only two input NANDs (or two input NORS).
• Design circuit diagrams that minimize the number of chips and gates using multiple-input NAND, NOR, and/or INVERTERS from equations.
• Use the XOR gate as a conditional inverter.
• Use the XNOR gate as a comparator.
• Design, build, test, measure and troubleshoot circuits using electronic gates interfaced to LEDs.

DE MORGAN'S THEOREMS

• Use De Morgan's theorems to minimize equations.
• Develop De Morgan's theorems from the duality of gates.
• Use De Morgan's theorems to minimize complex equations.

LOGIC CIRCUIT SIMPLIFICATION

• Simplify Boolean equations to produce more cost effective circuits.
• Confirm Boolean identities using switch logic, truth tables and other identities.
• Simplify equations using Boolean identities, theorems and rules.
• Simplify equations using Karnaugh Maps.

DIGITAL NUMBER SYSTEMS

• Express numbers in industry standard forms.
• Define the Octal number system.
• Define the Hexadecimal number system.
• Define the Binary Coded Decimal (BCD) system.
• Define the Gray code system.
• Define the ASCII system.
• Define parity.
• Convert between Binary, Octal, Hex, Decimal, and BCD.

BINARY NUMBER REPRESENTATION, ADDITION AND SUBTRACTION

• Represent unsigned binary numbers within registers of various sizes.
• Represent signed binary numbers (two’s complement method) within registers of various sizes.
• Change the sign of a signed binary number.
• Perform binary addition with signed and unsigned numbers.
• Perform binary subtraction with signed and unsigned numbers.
• Build and test a 4-bit adder/subtractor circuit.

DECODERS AND ENCODERS

• Describe the use of decoders and encoders.
• Define the decoder function.
• Develop equations for decoders.
• Investigate the 2-to-4 and 3-to-8 decoders.
• Define the encoder function.
• Develop equations for encoders.
• Develop expressions for a binary to 7-segment display decoder/driver.

LATCHES AND FLIP-FLOPS

• Analyze and implement latches and flip-flops.
• Define level, pulse, leading/trailing edge, transition.
• Analyze and design S-R and D latches using NOR/NAND gates.
• Implement a switch debouncer using a latch.
• Differentiate between latches and flip-flops.
• Analyze and utilize the following flip-flops: D, J-K.

Effective as of Fall 2013