Digital Logic Theory

1. Digital Logic Theory AWIM Series Lawndale High School Experiment 6 Dec, 2017

2. Number Systems • Numbers for Humans • The Decimal Number system • Base = 10 • Digits are 0-9 • Powers of ten for bigger numbers ( 104 + 103+ 102 + 101 + 100) • Ex. 456 = 4x102 + 5x101 + 6x100 = 400 + 50 + 6 • Numbers for Computers • The Binary Number system • Base = 2 • Digits are 0-1 • Powers for bigger numbers ( 25 + 24 + 23 + 22 + 21 + 20 ) • Ex. 54 = 1x25 + 1x24 + 0x23 + 1x22 + 1x21 + 0x20 = 32 + 16 + 4 + 2 • Bit = 1 digit • Byte = 8 Bits • Nibble = 4 Bits • Word = 16 Bits • Octal = 3 Bit group 0-7 • Hexadecimal = 4 Bit group 0-15 (0-9, A-F)

3. Logic is the fundamental language of the digital world of computers, calculators, digital instruments and digital electronics in general. It is the way machines talk with each other and with humans, providing responses for a given set of input conditions. • The term Logic, as used in this course, is a set of rules defining a predetermined output from a set of known inputs. • The most common logic in use today has two states, On (1or High); or off (0 or Low). • Digital logic today is implemented in multiple technologies, RTL, DTL, TTL, ECL, CMOS, etc. • The basic types of Logic in this course are Invert; AND; OR; NAND; and NOR. Using these basic types in combination can produce other logic functions (R-S and R-S-T Flip-Flops, etc). • In this lesson we will learn the symbols for each type of logic element, how to produce a “Truth Table” for each logic type, learn about Logic Notation and learn how to analyze combinational logic circuits. Digital Logic Theory

4. Digital Logic has a set of “threshold” voltages. Inputs below the lower threshold are considered a LOW or 0 input, while inputs above the upper threshold are considered a HIGH or 1 input. Voltages between the LOW and HIGH thresholds are ignored. • For the most common logic in use today which uses +5volts for its power (TTL, LS, ALS series), the lower threshold is about +0.4 volts and the upper threshold is about +2.4 volts. • Common Logic gates can have from 2 to 8 inputs. • Logic can be “positive logic” where a “1” is above the high threshold voltage, or “negative logic” where a “1” is below the low threshold voltage. • Logic can be designed to operate at very high speeds; ECL logic can run above 10Ghz. • High speed logic uses lower power supply voltages, 3.3 volts is common. Digital Logic Theory

5. IN OUT A A 0 1 C 1 0 Input Invert Symbol Truth Table • The Invert or “NOT” Gate Element Digital Logic Theory Output Equation C = • The Invert or NOT function provides the inversion or Opposite of the input. • This function is used alone and in series with other logic elements to form the negative of the element (OR + NOT = NOR).

6. IN A IN B OUT A 0 0 0 C B 1 0 0 Input 0 1 0 AND Symbol 1 1 1 Truth Table • The AND Gate Element Digital Logic Theory Output Equation C = A o B • The AND function provides a logic “1” on the output only when Both inputs are logic “1”. • This function is used in all types of logic and with the Invert element forms the NAND element .

7. IN A IN B OUT A 0 0 1 C B Output 1 0 1 Input 0 1 1 NAND Symbol 1 1 0 Truth Table • The NAND Gate Element Digital Logic Theory Equation C = A o B • The NAND function provides a logic “0” on the output only when Both inputs are logic “1”. • This function is used in all types of logic circuits.

8. IN A IN B OUT A C 0 0 0 B Output 1 0 1 Input 0 1 1 OR Symbol 1 1 1 Truth Table • The OR Gate Element Digital Logic Theory Equation C = A + B • The OR function provides a logic “1” on the output when Either input(s) are logic “1”. If we apply a NOT function to the output, we obtain the NOR gate. • This function is used in all types of logic circuits.

9. IN A IN B OUT A 0 0 1 C B Output 1 0 0 Input 0 1 0 NOR Symbol 1 1 0 Truth Table • The NOR Gate Element Digital Logic Theory Equation C = A + B • The NOR function provides a logic “0” on the output when Either input(s) are logic “1”. • This function is used in all types of logic circuits.

10. IN A IN B OUT A 0 0 1 B 1 0 1 Inputs Digital Logic Theory 0 1 0 A o B 1 1 1 Truth Table C Output B C = ( A o B ) + B = A + B Example 1 – combinational logic

11. Combinational logic circuit using two NAND gates. “Set” Input A C Digital Logic Theory Output C “Reset Input B Output R-S “Set-Reset Flip Flop • This circuit provides a “Bi-Stable” switch function, Alternating from one state to the other based on the inputs.

12. Input Wave-shaping circuit using two NAND gates C Digital Logic Theory Output C Output • This circuit changes a Sine wave input into a Square wave using the R-S latch function.

13. Name:__________ Date:________ • A input of 0.25volts to standard 5v logic equals a “1” T F • The notation for a two input OR gate is A + B. T F • Most new automobiles contain digital logic T F • The term TTL stands for Diode-Transistor-Logic T F • A AND gate can have only two inputs T F • A OR gate and a NOT gate can be combined to form a: a) problem gate b) NAND gate c) NOR gate d) Invert gate • If we put NOT gates on both inputs to a two input AND gate we have a: a) NAND gate b) NOR gate c) maybe gate d) water gate • How many input combinations can a Four input AND gate handle: a) 4 b) 16 c) 8 d) 12 • What is the normal HIGH Threshold voltage for 5volt logic: a) 1.2 volts b) 5.0 volts c) 3.3 volts d) 2.4 volts Homework - Digital Logic

14. IN A IN B OUT A 0 0 B 1 0 Inputs Homework - Digital Logic 0 1 1 1 Truth Table C Output C = Problem 10 – Write the equation for the output of the circuit above and fill in the Truth Table.

15. IN A IN B IN C OUT A 0 0 0 B 1 0 0 Homework - Digital Logic 0 1 0 1 1 0 Inputs 0 0 1 1 0 1 0 1 1 1 1 1 D C Output Truth Table D = Problem 11 – Write the equation for the output of the circuit above and fill in the Truth Table.