Digital circuit simplification, digital circuit simplification formula

Digital circuits, with AND gates, or gates, and NAND gates.

First, with the door. And gate (English: and gate) is also known as "and circuit", logical "product", logical "and" circuit.

It is the basic logic gate circuit that performs the AND operation. There are multiple inputs, one output. The output is high when all inputs are high (logic 1) at the same time, otherwise the output is low (logic 0).

The AND gate is a circuit that implements the logic "multiplication" operation, with two or more inputs and one output (general circuits have only one output, and ECL circuits have two outputs). The circuit output is high (logic "1") only if all inputs are high (logic "1"), otherwise the output is low (logic "0"). 1] The second input is the mathematical logical expression of the gate:

y = ab。

II. or Door. Or gate, also known as or circuit, logic, and circuit. If only one of the conditions is satisfied, an event will occur, and this relationship is called an "or" logical relationship.

A circuit with an OR logic relationship is called an OR gate. or gate has multiple inputs, one output, as long as one of the inputs is high (logic "1"), the output is high (logic "1"); The output is low (logic "0") only when all inputs are low (logic "0").

OR gate is a circuit that implements logic addition, also known as logic and circuit, referred to as OR gate. This circuit has more than two inputs and one output. As long as one or more of the inputs are "1", or the output of the gate is "1".

The output is only "0" if all inputs are "0"[1]. The mathematical-logical expression for the OR gate is:

3. Non-door. NAND gate (English: not gate), also known as non-circuit, inverter, inverter, logic negation circuit, referred to as NAND gate, is the basic unit of logic circuit.

NOR gates have one input and one output. The output is low (logic 0) when its input is high (logic 1) and high when its input is low. That is, the level states at the input and output are always inverted.

The logic function of NAND gate is equivalent to NAND in logic algebra, and the circuit function is equivalent to inverting, and this operation is also called non-operation.

I hope I can help you with your doubts.

<> I did it a little bit and turned it into this, I don't know if it's right.

Digital circuit formulation: Simplification of commonly used formulas.

Equation 1: ab+ab=a

Equation 2: a+ab=a

Equation 3: a+ab=a+b Prove: Left = a+(ab+ab)=a+b If the inverse variable of one variable is a factor of another formula, then this inverse variable is redundant.

Knowledge Expansion: A circuit that uses digital signals to perform arithmetic and logical operations on digital quantities is called a digital circuit, or digital system. Because it has logic operation and logic processing functions, it is also called a digital logic circuit.

Modern digital circuits are constructed from several digitally integrated devices made in semiconductor processes. A logic gate is the basic unit of a digital logic circuit. Memory is a digital circuit used to store binary data.

On the whole, digital circuits can be divided into two categories: combinatorial logic circuits and sequential logic circuits.

Divided by function:

Combinatorial logic circuits.

Referred to as a combinatorial circuit, it is composed of the most basic logic gate circuits. The characteristic is that the output value is only related to the input value at that time, that is, the output is uniquely determined by the input value at that time.

The circuit does not have a memory function, and the output state changes with the change of the input state, similar to resistive circuits, such as adders, decoders, encoders, data selectors, etc.

Sequential logic circuitry.

Referred to as a sequential circuit, it is a circuit composed of the most basic logic gate circuit plus a feedback logic loop (output to input) or a device, and the most essential difference from the combined circuit is that the sequential circuit has a memory function. Sequential circuits are characterized by the fact that the output depends not only on the input value at the time, but also on the past state of the circuit.

It is similar to the inductor or capacitor circuit containing energy storage components, such as flip-flops, latches, counters, shift registers, memory and other circuits are typical devices for sequential circuits.

According to whether the circuit has integrated components, it can be divided into discrete component digital circuit and integrated digital circuit.

According to the integration degree of integrated circuits, they can be divided into small-scale integrated digital circuits (SSI), medium-scale integrated digital circuits (MSI), large-scale integrated digital circuits (LSI) and ultra-large-scale integrated digital circuits (VLSI).

According to the semiconductor devices that make up the circuit, it can be divided into bipolar digital circuits and unipolar digital circuits.

Yours d'It's out of nothing.

It is simplified as follows: b'+a'c+ac'd'+ac'db'+a'c+ac'(d'+d)=b'+a'c+ac'

The reason why you have more d', because of simplification.

There is a'c+ac'd'=a'c+d'and a'c+ac'd=a'c+ac'。

This is wrong.

Simply a'c+ac'd'and a'c+ac'D is already the simplest form, and you can't get your results.

You can see it very clearly with a Carnot diagram.

Digital Circuits Simplification of Logic Functions Formulation Simplification.

1.Merger: ab + ab' = a

Merge the two items into one, and delete b and b'

2.Absorption: A + AB = A

The short term absorbs the long term.

3.Elimination: ab + a'c + bc = ab + a'c

It can be expanded to: ab + a'c + bcd = ab + a'c

4.Factor elimination method: a + a'b = a + b

The short term removes the opposite term of the long term.

It can also be understood here that a is seen as a*(1+b), i.e., a+ab+a'b

5.Matching method: The basic formula is raiding a + a = a

Expand. Other common formulas:

The product of the two terms is added, and one of them is factored by the other, and the term can be deleted;

The product terms of the two terms are added together, and the inversion of one term is the factor of the other term, which can be eliminated;

If they contain the two factors b and b' respectively and the other factors are the same, then the two must be combined and b,b' can be eliminated;

When the sum of the variable a and the sum containing the variable a is multiplied, the result is a, and the sum can be eliminated;

If the two product terms contain two factors, a and a', respectively, and the remaining factors of the two product terms form the third product term, then the third product term is redundant and can be eliminated and further promoted: ab+a'c+bcd=ab+a'c;

When a is a non-multiplicative of a product term, and a is a factor of the product term, then a factor can be eliminated;

a'(ab)'=a' When a' is a non-multiplication of a product term, and a is a factor of the product term, the result is equal to a'

Digital Circuits Simplification of Logic Functions Formulation Simplification.

1.Merger: ab + ab' = a

Merge the two items into one, and delete b and b'

2.Absorption: A + AB = A

The short term absorbs the long term.

3.Elimination: ab + a'c + bc = ab + a'c

It can be expanded to: ab + a'c + bcd = ab + a'c

4.Factor elimination method: a + a'b = a + b

The short term removes the opposite term of the long term.

It can also be understood here that a is seen as a*(1+b), i.e., a+ab+a'b

5.Matching method: The basic formula is raiding a + a = a

Expand. Other common formulas:

The product of the two terms is added, and one of them is factored by the other, and the term can be deleted;

The product terms of the two terms are added together, and the inversion of one term is the factor of the other term, which can be eliminated;

If they contain the two factors b and b' respectively and the other factors are the same, then the two must be combined and b,b' can be eliminated;

When the sum of the variable a and the sum containing the variable a is multiplied, the result is a, and the sum can be eliminated;

If the two product terms contain two factors, a and a', respectively, and the remaining factors of the two product terms form the third product term, then the third product term is redundant and can be eliminated and further promoted: ab+a'c+bcd=ab+a'c;

When a is a non-multiplicative of a product term, and a is a factor of the product term, then a factor can be eliminated;

a'(ab)'=a' When a' is a non-multiplication of a product term, and a is a factor of the product term, the result is equal to a'

q3* = q3q2' + q2q1q0（q3 + q3'）

q3q2' + q2q1q0 ≠ q3q2' + q2q1q0 q3'

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