Digital ICs Education

The Rules of Binary Addition Adding binary numbers is a very simple task, and very similar to the longhand addition of decimal numbers. As with decimal numbers, you start by adding the bits (digits) one column, or place weight, at a time, from right to left. Unlike decimal addition, there is little to memorize in the way of rules for the addition of binary bits: 0 + 0 = 0 1 + 0 = 1 0 + 1 = 1 1 + 1 = 10 1 + 1 + 1 = 11 Just as with decimal addition,

A demultiplexer, sometimes abbreviated dmux, is a circuit that has one input and more than one output. It is used when a circuit wishes to send a signal to one of many devices. This description sounds similar to the description given for a decoder, but a decoder is used to select among many devices while a demultiplexer is used to send a signal among many devices. A demultiplexer is used

Serial-in, serial-out shift registers delay data by one clock time for each stage. They will store a bit of data for each register. A serial-in, serial-out shift register may be one to 64 bits in length, longer if registers or packages are cascaded. Below is a single stage shift register receiving data which is not synchronized to the register clock. The “data in” at the D pin of the type D

If the output of a shift register is fed back to the input. a ring counter results. The data pattern contained within the shift register will recirculate as long as clock pulses are applied. For example, the data pattern will repeat every four clock pulses in the figure below. However, we must load a data pattern. All 0‘s or all 1‘s doesn’t count. Is a continuous logic level from

Larger Karnaugh maps reduce larger logic designs. How large is large enough? That depends on the number of inputs, fan-ins, to the logic circuit under consideration. One of the large programmable logic companies has an answer. Altera’s own data, extracted from its library of customer designs, supports the value of heterogeneity. By examining logic cones, mapping them onto LUT-based nodes and sorting them by the number of inputs that

Knowing how to generate Gray code should allow us to build larger maps. Actually, all we need to do is look at the left to right sequence across the top of the 3-variable map, and copy it down the left side of the 4-variable map. See below. Reductions of 4 Variable K Maps The following four variable Karnaugh maps illustrate the reduction of Boolean expressions too tedious for Boolean algebra. Reductions

PARTS AND MATERIALS 4511 BCD-to-7seg latch/decoder/driver (Radio Shack catalog # 900-4437) Common-cathode 7-segment LED display (Radio Shack catalog # 276-075) Eight-position DIP switch (Radio Shack catalog # 275-1301) Four 10 kΩ resistors Seven 470 Ω resistors One 6 volt battery Caution! The 4511 IC is CMOS, and therefore sensitive to static electricity! CROSS-REFERENCES Lessons In Electric Circuits, Volume 4, chapter 9: “Combinational Logic Functions” LEARNING OBJECTIVES How to use the 4511 7-segment decoder/display driver IC Gain familiarity with

Why learn about Karnaugh maps? The Karnaugh map, like Boolean algebra, is a simplification tool applicable to digital logic. See the “Toxic waste incinerator” in the Boolean algebra chapter for an example of Boolean simplification of digital logic. The Karnaugh Map will simplify logic faster and more easily in most cases. Boolean simplification is actually faster than the Karnaugh map for a task involving two or fewer Boolean variables. It

So far, we’ve only been able to escape the sheer volume of components in the flash converter by using a DAC as part of our ADC circuitry. However, this is not our only option. It is possible to avoid using a DAC if we substitute an analog ramping circuit and a digital counter with precise timing. The is the basic idea behind the so-called single-slope, or integrating ADC. Instead

One of the more advanced ADC technologies is the so-called delta-sigma, or ΔΣ (using the proper Greek letter notation). In mathematics and physics, the capital Greek letter delta (Δ) represents difference or change, while the capital letter sigma (Σ) represents summation: the adding of multiple terms together. Sometimes this converter is referred to by the same Greek letters in reverse order: sigma-delta, or ΣΔ. In a ΔΣ converter, the analog input voltage signal is connected

In ladder logic symbolism, an electromechanical relay coil is shown as a circle, and the contact(s) actuated by the coil as two parallel lines, almost like a capacitor symbol. Given this knowledge, interpret the following ladder logic diagram: How do we know which relay contact is actuated by which relay coil? How does this convention differ from that of standard electrical/electronic schematic diagrams, where the relay coil is

Boolean algebra finds its most practical use in the simplification of logic circuits. If we translate a logic circuit’s function into symbolic (Boolean) form, and apply certain algebraic rules to the resulting equation to reduce the number of terms and/or arithmetic operations, the simplified equation may be translated back into circuit form for a logic circuit performing the same function with fewer components. If equivalent function may be

Guidelines to Series-Parallel Combination Circuit Analysis The goal of series-parallel resistor circuit analysis is to be able to determine all voltage drops, currents, and power dissipations in a circuit. The general strategy to accomplish this goal is as follows: • Step 1: Assess which resistors in a circuit are connected together in simple series or simple parallel. • Step 2: Re-draw the circuit, replacing each of those series or parallel resistor combinations identified in

We can construct simple logic functions for our hypothetical lamp circuit, using multiple contacts, and document these circuits quite easily and understandably with additional rungs to our original “ladder.” If we use standard binary notation for the status of the switches and lamp (0 for unactuated or de-energized; 1 for actuated or energized), a truth table can be made to show how the logic works: Now, the lamp will come on if

PARTS AND MATERIALS One 9V Battery Battery Clip (Radio Shack catalog # 270-325) Mini Hook Clips (soldered to Battery Clip, Radio Shack catalog # 270-372) A Watch with a second hand/display or a Stop Watch A wire, 11/2” to 2” (3.8 mm to 5 mm) long, folded in half (shown as red wire in illustration) U1 - 555 timer IC (Radio Shack catalog # 276-1723) D1 - Red light-emitting diode (Radio Shack catalog # 276-041 or equivalent) D2

Perhaps the most important consideration of an ADC is its resolution. Resolution is the number of binary bits output by the converter. Because ADC circuits take in an analog signal, which is continuously variable, and resolve it into one of many discrete steps, it is important to know how many of these steps there are in total. For example, an ADC with a 10-bit output can represent up to 1024 (210) unique

It is sometimes useful in logic circuits to have a multivibrator which changes state only when certain conditions are met, regardless of its S and R input states. The conditional input is called the enable, and is symbolized by the letter E. Study the following example to see how this works: When the E=0, the outputs of the two AND gates are forced to 0, regardless of the states of either

For reference, this section introduces the terminology used in some texts to describe the minterms and maxterms assigned to a Karnaugh map. Otherwise, there is no new material here. Σ (sigma) indicates sum and lower case “m” indicates minterms. Σm indicates sum of minterms. The following example is revisited to illustrate our point. Instead of a Boolean equation description of unsimplified logic, we list the minterms. f(A,B,C,D) = Σ

PARTS AND MATERIALS 4001 quad NOR gate (Radio Shack catalog # 276-2401) Eight-position DIP switch (Radio Shack catalog # 275-1301) Ten-segment bar graph LED (Radio Shack catalog # 276-081) One 6 volt battery Two 10 kΩ resistors Two 470 Ω resistors Two 100 Ω resistors Caution! The 4001 IC is CMOS, and therefore sensitive to static electricity! CROSS-REFERENCES Lessons In Electric Circuits, Volume 4, chapter 3: “Logic Gates” Lessons In Electric Circuits, Volume 4, chapter 10: “Multivibrators” LEARNING OBJECTIVES The effects of positive feedback in

What do you think this logic buffer gate will do, with the output signal “feeding back” to the input? What do you think this buffer will do when each input switch is separately pressed? Why does the second buffer circuit need a resistor in the feedback loop?