REPORT FOR LAB C1: DIGITAL LOGIC

Nathaniel Kan2/10/02

ABSTRACT:

In the Digital Logic lab we became familiar with integrated circuits in the form of logic gates. We verified the truth table of a NAND gate, and constructed and verified the truth tables of an OR gate and an EXCLUSIVE OR gate. We then constructed and verified the truth tables of an RS latch, a half adder circuit, and a counting circuit, which was connected to a seven segment LED display. We found all these circuits to work as according to their pre-determined truth tables.

PURPOSE:

The purpose of the Digital Logic lab was to familiarize ourselves with the use of digital logic gates. We first became familiar with the ranges of voltages representing high and low, the use of a logic breadboard, and the functions of NOT, NAND, and NOR gates. We then were to construct several more complex circuits, including a memory circuit, an arithmetic circuit, and a counting circuit.

PRINCIPLES:

In this lab we were primarily working with Integrated Circuits in the Transistor-Transistor-Logic family. These circuits use two logic levels to report results, corresponding to two voltage ranges:

1 = True = High = approx. 2.4 to 5+ V0 = False = Low = approx. 0 to 0.8 V

For this experiment we use a breadboard, which contains many common circuit elements as well as a holding area which provides easy wiring into the IC chips (See C1 Lab handout page 3 for diagram).

PROCEDURE:

We began by checking the functionality of all components of the breadboard including the power source, the LEDs, the clock signal, and the switches. We then tested the NAND gates on one of the IC circuits by connecting their inputs to two switches, and their outputs to an LED. Pin 14 and Pin 7 are connected to the positive and ground terminals of the power supply, respectively. We then verified that the actual truth table was a duplicate of the predicted one (See Data section).

Next we constructed the OR gate and the EXCLUSIVE OR gate (See Lab book page 53 for diagrams). The OR gate produces a result of True if either input A or B is True, or both are True. The EXCLUSIVE OR gate produces a result of True if input A or B is True, but

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False if A and B are both True or both False. We then verified that their truth tables matched up to the theoretical ones. We then used our knowledge of IC circuits to design a circuit to solve the Part 4 Logic Problem (See Data section).

The next circuit was the RS latch (see Lab book page 54 for diagram). This circuit, because it is a feed back loop between two NAND gates, has two stable settings, Q = 0 and Q’ = 1, or Q = 1 and Q’ = 0. These settings will be maintained in “memory” until a new stable setting is inputted. If both R and S inputs are set to True, the circuit will continue in its stable 1,0 or 0,1 setting. If both inputs are set to False, then the circuit will temporarily go high, but then return to its stable setting.

Next we constructed a half-adder digital arithmetic circuit (Lab book page 55). This circuit adds two binary digits (1 or 0) together in binary, where the QF is the tens digit and C is the unit digit. We then verified the circuits’ truth table.

The last circuit we constructed was a counting circuit, using the 7490 chip. By connecting the A B C D outputs to LEDs, the powered chip counts from 0 to 9 in binary through turning the LEDs on and off (see C1 Lab handout page 7 for diagram). After verifying this, we then connected the counting circuit to a seven segment LED. The LEDs are arranged such that when lit properly they form numbers from 0 to 9. The circuits inside the LED holding box allowed the 7490 chip to be connected directly to the box through four contacts, which then connected through logic gates to the LEDs, lighting the correct LEDs to produce the numbers 0 through 9 in correct succession.

DATA:

OR Gate Truth Table

A B QA QB QF

0 0 1 1 0

1 1 0 0 1

1 0 0 1 1

0 1 1 0 1

EXCLUSIVE OR Gate Truth Table

A B Q1 Q2 Q3 QF

0 0 1 1 1 0

1 1 0 1 1 0

0 1 1 1 0 1

1 0 1 0 1 1

Part 2C Problem-Solving Circuit Truth Table (See Lab book page 54 for circuit diagram)

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A B C Q1 Q2 QF

0 1 1 1 0 1

1 0 1 1 0 1

1 1 1 1 0 1

0 0 1 0 1 0

0 1 0 1 1 0

1 0 0 1 1 0

1 1 0 1 1 0

0 0 0 0 1 0

RS Latch Truth Table

R S QR QS

0 0 1 1

0 1 0 1

1 0 1 0

1 1 Q Q

Arithmetic Circuit Truth Table

A B Q1 Q2 Q3 QF C

0 0 1 1 1 0 0

1 0 0 1 1 0 1

0 1 0 1 1 0 1

1 1 1 0 1 1 0

RESULTS:

When the LED is connected through the clock signal, the diode flashes at the same frequency as the signal. This is because the diode does not allow the negative current to flow, but does allow the positive current through. This means that the current oscillates between off and on at the frequency of the clock.

All the circuits we constructed matched their logically predicted truth tables (after we had corrected all construction errors). In constructing the circuit to solve the Part 2C problem, we used an OR gate with the two inputs being A and B, and then used the result of that, Q1 and C in a NAND gate which fed its result, Q2, into both inputs of another NAND gate, which outputs the answer, Q3.

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