4.3 Logic Gates

Gates packaged as ICs contain circuits that are capable of performing logical operations based on input states (5V represents a logic state of 1 and 0V represents a logic state of 0). The output voltage is based on the voltage of the inputs and the logical operation of the gate. For example, if the input voltages on an AND gate are 5V and 0V, then output voltage will be 0V. This is based on the logical operator AND.

The internal workings of a gate are based on combinations of diodes, transistors, resistors, and other circuit devices. The gate function can be achieved by using different combination of circuit devices. The circuit devices are arranged such that they perform the various logical operations. The following are some types of circuit component arrangements that can produce the desired logical output. Though the functional output is the same, the performance can vary under different conditions. The different arrangement of devices that are capable of producing logic output can be categorized as:

• DL - Diode logic
• DTL – Diode-transistor logic
• TTL – Transistor-transistor logic
• RTL – Resistor-transistor logic

Earlier in section 4.2 it was seen how transistors can act as switches and perform logic operations. Now consider the case of diode logic, where logic functionality is obtained using diodes and resistors. The figure 4.40 shows how a pair of diodes can be arranged to perform the OR logic function. When the voltage of A and B is at 0V then the output voltage will be 0V. Similarly, when the voltage at A is 5V and B is 0V then the voltage on the output becomes 5V, assuming the diode provides no resistance to cause a drop in the voltage.

Fig. 4.40. Diode arrangement that produces an OR function

The table on the right shows the voltage characteristics of the circuit in figure 4.40, and from it can be seen that the circuit performs the OR operation. Similarly it is possible to achieve the AND operation by using a different arrangement of the diodes and the resistor Again it can be seen that the circuit in figure 4.41 performs the AND logical operation.

Fig. 4.41. Diode arrangement that produces an AND function

Using different arrangements of circuit components the various logic functions can be achieved electrically. In the field of computing the interest is more in the logic functionality than the actual implementation of it using different components. Therefore, each logic function is represented symbolically ignoring the implementation method. The following table shows the symbols used for the different gates along with their logical operation.

Table 4.6. Logic gate symbols

Of the various different implementation of gates, the most popular is the TTL. The TTL implementation also has variations within it, so it is called the TTL family of logic gates. A TTL logic gate IC is identified by its 7400 series numbering. Therefore, all TTL logic gate IC’s will begin with 74, and each type of gate based on its output characteristic will have different ending digits. To designate various members within the TTL family, letters are added between the first two and last two digits. For example, 7432 would be a standard TTL gate, 74L32 would be a low power TTL gate, and 74H32 would be a high speed TTL gate. All the members of the family will perform the same logic function, but have different electrical performance characteristics such as power consumption, voltage tolerances, etc. The table below shows the TTL IC numbers for the various types of logic gates.

Table 4.7. TTL IC numbers.

The input-output characteristics of a gate is the key for most applications of gates.  Therefore, internal workings of the gate can be neglected at the present. Each gate is represented using a different symbol with the input and output terminals. The supply voltage required to make the device work is not usually represented on the symbol because it remains constant, at 5V for the TTL standard. The constant supply voltage is provided externally by a voltage source. Figure 4.42 shows a 7408 AND gate IC and its pinout.

Pins 7 and 14 are used to supply the gate IC with power. In TTL family of ICs pin 14 V_cc is +5V supply voltage and pin 7 GND is 0V or ground. This means that pin 14 is connected to the positive terminal of a voltage source and pin 7 is connected to the negative terminal. In this case pins 1, 2, and 3 form an AND gate. Therefore, if pin 1 is connected to +5V and pin 2 is connected to 0V (ground) then the voltage on pin 3 will be 0V. On the other hand, if pin 1 is connected to +5V and pin 2 is also connected to +5V, then the voltage on pin 3 will be +5V as shown in figure 4.43. In this case the LED will be on. 

4.43

In a standard TTL logic gate IC, logic state 1 is any voltage between (3.5V and 5V) and logic state 0 is any voltage between (0V and 3.5V). This range should be taken into consideration when building circuits, because devices that are connected to the gates directly could cause the voltage to drop below the 3.5 limit and cause a change in the logic state to occur.

It is possible to have gates that have more than two inputs. Such gates can be constructed using multiple two input gates, but multi input gates are less cumbersome to wire and use for many applications. For example, a circuit that has three inputs and is only 1 when all the inputs are 1 would be an example of such a gate as shown below.

The gate on the right performs the same function as the two input AND gate combination shown on the left. The TTL family of IC’s provide such gates to facilitate the construction of digital circuits. The TTL 7410 IC (see table 4.7) is an example of such an implementation. Similarly it is possible to have three input and multi input versions of some of the other gates.

Design Considerations

When designing logic circuits the type of technology used to implement the logic function can play a significant role in the performance. Some of the issues that must be taken into consideration before selecting a type of technology are:

Operating range : Different technologies will have different operating ranges in terms of voltages, current, and temperature.

Power rating: The power consumption by the different technologies will vary. This is important when a device is operated by a battery. Lower the power consumption, longer the operating time of a battery powered the device. Power consumption is also important in controlling device heating. Electrical energy is converted to heat energy in electrical devices, so when power consumption is high a lot of heat is generated.

Gate delay: When the input of a logic gate changes the output logic state does not change immediately, but instead it takes a small amount of time for the output state to change to its new value. This delay is different for different technologies.

Material cost: As always cost is an important driving factor in large scale design. Again the different technologies will have different costs. For example, TTL gates are relatively inexpensive when compared to other types like MOS and ECL gates.

Fan out: Fan out is a term used to describe the number of consecutive gates between the input and output. Due to electrical limitations there is a limit to the fan out of gates, and the fan out limit varies from one technology to another.

Given these differences in technologies it is important to keep them in mind when designing and implementing logic circuits.

Negative Logic

The representation of logic using electrical signals thus far has been based on the idea that logic state 1 is assigned a high voltage (+5V) and logic state 0 is assigned a low voltage (0V); this assignment is called positive logic. The interchanging of this assignment is called negative logic. In negative logic, logic state 1 is assigned a low voltage (0V) and logic state 0 is assigned a low voltage (+5V). The reversal of the voltage assignment does not in any way limit our ability to create circuits that will perform the various logic functions, but it is not exactly the same as positive logic. Negative logic becomes a useful tool when working with NAND and NOR gates, thus providing a technical advantage in digital circuit design. Given the two methods of representation, positive and negative logic, care must be taken to ensure that confusion is not created because the two methods will give two different logic interpretations, as shown in the table below.

Table 4.9. Input – output voltage pattern

From the truth tables it can be seen that the same voltages are interpreted differently in positive logic and negative logic.  The positive logic interpretation leads to an OR logical operation, and the negative logic interpretation leads to an AND logical operation. In this case it can be seen that a positive logic OR and a negative logic AND are equivalent because they both represent the same voltage pattern. Due to the fact that positive and negative logic give different logical results for the same voltage, care must be taken to avoid confusion. Confusion between positive and negative logic is avoided by using a different, but similar set of symbols.

Table 4.10. Negative Logic gate symbols

4.3 Practice Questions  1.     A student connects a 5V supply to a 7408 TTL IC. If the student connect 5V to pin 1, determine the voltages on pins 2, 3, 4, 5, and 6. 2.     What are the symbols for the following gates?         a. NOR                b. XOR                 c. AND d. NAND   e. OR 3.     What are the voltage specification of the TTL logic gates? 4.    What gate in negative logic is the positive logic XOR gate equivalent to? 5.    Using truth tables show that positive logic NAND is equivalent to negative logic NOR? 6.    What feature on logic gate symbol can be used to determine if a gate is positive or negative logic? 7.    Investigate the differences between a CMOS gate and a TTL gate.