Extra Class question of the day: digital circuits, flip-flops

Digital circuits are used for a variety of functions in modern amateur radio equipment. Unlike analog circuits, the output voltage of an ideal digital circuit can only be one of two values. One of these voltages—normally a positive voltage—represents a digital 1. The other value—normally near 0 V—represents a digital 0.

This type of logic is generally called positive logic. Positive Logic is the name for logic which represents a logic “1” as a high voltage. (E7A11) The logic may be reversed, though. That is to say that a high voltage may represent a logic 0. Negative logic is the name for logic which represents a logic “0” as a high voltage. (E7A12)

The microcomputers that control today’s transceivers, for example, are very complex digital circuits. These complex digital circuits are made by combining many smaller building blocks called logic gates. These gates perform basic digital logic functions.

NAND Truth Table

Table E7-1. This two-input NAND truth table show the output (Q) for each combination of inputs (A,B).

One of the most basic digital circuits in the NAND gate. The logical operation that a NAND gate performs is that it produces a logic “0” at its output only when all inputs are logic “1.” (E7A07)

This logical operation can be described by a truth table. A truth table is a list of inputs and corresponding outputs for a digital device. (E7A10) Table E7-1 shows a truth table that describes the operation of a two-input NAND gate. A and B are the two inputs; Q is the output.

NOR Truth Table

Table E7-2.

Other types of gates perform different logical functions. The logical operation that an OR gate performs is that it produces a logic “1” at its output if any or all inputs are logic “1.” (E7A08) Table E7-2 shows a truth table that describes the logical operation of an OR gate.

The logical operation that is performed by a two-input exclusive NOR gate is that it produces a logic “0” at its output if any single input is a logic “1.” (E7A09) Table E7-3 shows a truth table that describes the logical operation of an OR gate.

XNOR Truth Table

Table E7-3.

Flip-flops are circuits that are made from combinations of logic gates. The output of a flip-flop is not entirely dependent on its inputs; it is also dependent on the current value of its output.

As an example, let’s look at the SR or RS flip-flop. An SR or RS flip-flop is a set/reset flip-flop whose output is low when R is high and S is low, high when S is high and R is low, and unchanged when both inputs are low. (E7A13) So, once set to a particular value, the output will not change when both inputs are set to low.

Some flip-flops are clocked. That is to say that they only change states when a clock signal input changes states. A D flip-flop is an example of this type of flip-flop. A D flip-flop is a flip-flop whose output takes on the state of the D input when the clock signal transitions from low to high. (E7A15) A JK flip-flop is a flip-flop similar to an RS except that it toggles when both J and K are high. (E7A14)

Another type of flip-flop is the T flip-flop. The T flip-flop is so called because for each transition from low to high on the flip-flop’s T input, the output “toggles” from 0 to 1 if the output was already at 0, and from 1 to 0 if the output was already at 1. Two output level changes are obtained for every two trigger pulses applied to the input of a T flip-flop circuit. (E7A02) See figure E7-1 below.

T Flip Flop

The output of a T flip-flop changes state every time a clock pulse appears on the T input. This effectively divides the input frequency by a factor of two.

A flip-flop can divide the frequency of a pulse train by 2. (E7A03) Consequently, 2 flip-flops are required to divide a signal frequency by 4. (E7A04)

A flip-flop is a bistable circuit. (E7A01) What that means is that its output is stable in either state. An astable multivibrator is a circuit that continuously alternates between two states without an external clock. (E7A05) In other words, it is an oscillator.

A monostable circuit is one that is stable in one state but not the other. One characteristic of a monostable multivibrator is that it switches momentarily to the opposite binary state and then returns, after a set time, to its original state.(E7A06) A trigger pulse causes the monostable vibrator to switch to the unstable state, and it stays in that state for a set period, no matter how long the trigger pulse.

Resources
Wikipedia: Multivibrator (https://en.wikipedia.org/wiki/Multivibrator)

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