Binary translator: An introduction with examples

Translation tools are always very papular and convenient for different people to understand the concept in their native language. We also have an experience with such benefit tools to reduce the difficulty level and enhance the conceptual understanding.

In this article, we will discuss a translator that enhances the security of our data and some examples which are brief explanations of how we convert and decode the given input.

 What is the binary system?

The binary system is the system of numbers whose base is 2. Only two digits are used which are 0 and 1. This system is applicable in physics, to say the system is on or off. We have already converted a number system to another number system.

We have the basic knowledge of the conversion of binary to decimal and decimal to binary systems.

Decimal to binary:

If we have a number that is given in the form of decimal means in the system of base 10 we can convert it into the binary system. We have to divide by 2 to the given decimal number and write the reminders.

e.g. (20)10 = (10100)2

What is the ASCII?

The ASCII is the short form of the American Standard Code for Information Interchange. It is the standard for character encoding in electric communication. Most of the character encoding is based on the ASCII. ASCII is the language of the codes which are special means in the native language. We use the ASCII system to code the binary language into English.

Binary to English:

We use binary code and translate it into English by using ASCII. We have a binary number that converts into English. We have some binary codes that we have to translate into English.

Example 1:

Binary code

01110111 01100101 00100000 01100001 01110010 01100101 00100000 01110100 01101000 01100101 00100000 01110011 01110100 01110101 01100100 01100101 01101110 01110100 01110011 00100000 01101111 01100110 00100000 01100111 01110010 01100001 01100100 01100101 00100000 00110111 00101110

Translate

we are the students in grade 7.

Example 2:

Binary code

01010111 01100101 00100000 01110000 01101100 01100001 01111001 00100000 01110100 01101000 01100101 00100000 01100111 01100001 01101101 01100101 00100000 01100110 01101111 01110010 00100000 00110001 00110000 00100

000 01101000 01101111 01110101 01110010 01110011 00101110 00001010

Translate:

We play the game for 10 hours.

To convert the computer binary system into the English language we can use an ASCII table which is very time taking to translate. To save your time and decode the given binary code into English, use a binary translator.

We write a binary code on the left side and press the to text button to decode the 

Example 3:

English letter	ASCII decimal	Binary string
d	100	01100100
o	111	01101111
g	103	01100111

01100100 01101111 01100111 = dog

Why is ASCII significant?

Because ASCII is now the same on all computers, it serves as the connection between our computer's screen and hard drive.

Use of ASCII:

Computer text is converted to human text using ASCII.

Every computer uses binary, which is a series of 0s and 1s. However, computers also have their own versions of languages, just as English and Spanish can use the same alphabet yet have entirely distinct words for similar items.

Application of binary numbers:

Since then, many different applications have made use of the binary number system. This includes handling multiple digital signal processing applications, capturing high-end music and HD movies, storing millions of data entries, and processing images. A binary converter is a tool that can guarantee the success of these applications.

Summary:

In this article, we have learned about the binary system, ASCII, and translated the binary system into the English language. Now after reading the above post, you can convert any binary code into English language and enhance the safety of your data.

Parallel Resistors | Formula Of Parallel Resistors

I have discussed series-connected resistors, now it's time to learn more about parallel-connected resistors. First of all, I would like to recall the definition of parallel circuits.

Two components are connected in such a way that they have two common terminals. A parallel circuit is one in which all components are connected in parallel.

Similarly, two resistors are connected in parallel when they have two common terminals. It is often confusing to recognize parallel circuits. Beginners should redraw the circuits.

Properties of parallel circuits:

• Voltage remains the same in every parallel-connected resistor
• Current divides proportionally to all resistors. The larger the resistance value the less will be the current flowing through the resistor

Formula Of Parallel Resistance:

Figure 1

Let's consider the circuit in figure 1. A voltage source is in parallel with three resistors. As I discussed above, the voltage remains the same in each parallel-connected resistor. The current divides among the resistances. So, with the help of Ohm's law, we can easily evaluate the current flowing through each resistor.

Current through R1:

i1 = v/R1

Current through R2:

i2 = v/R2

Current through R3:

i3 = v/R3

The total current flowing through the circuit:

i = i1 + i2 + i3

i = v/R1 + v/R2 + v/R3

i = v{1/R1 + 1/R2 + 1/R3}

i/v = 1/R1 + 1/R2 + 1/R3

From Ohm's law i/v = 1/Req. Substitute in the above equation

1/Req = 1/R1 + 1/R2 + 1/R3

Req = R1 || R2 || R3

The easiest way to solve the above equation is the reciprocal method. Solve individual fractions first and then simply add them.

Solved Examples:

Example #1:

Determine total or equivalent resistance and the current flows through each resistor with the help of Ohm's law.

Equivalent Resistance: It is easy to solve with the help of the above formula.

1/Req = 1/R1 + 1/R2 + 1/R3

1/Req = 1/1k + 1/2k + 1/3k

Req = 545.5 Ω

Current:

Let,

i1 = current flowing through R1

i2 = current flowing through R2

i3 = current flowing through R3

Voltage remains in all three resistors as they are connected in parallel combination

.

i1 = v1/R1

i1 = 10/1000

i1 = 10mA

i2 = v1/R2

i2 = 10/2000

i2 = 5mA

i3 = v1/R3

i3 = 10/3000

i3 = 3.33mA

Conclusion:

• The total/equivalent resistance of the circuit will be less than the smallest resistance present in the parallel circuit
• If we are continuously adding parallel resistance, the total resistance of the circuit decreases
• The larger the resistance, the lower will be the current. Or you can say current will always flow through the less resistive path
• There is another simpler method of finding current through parallel resistors. This method is known as the Current Divider Rule

K-Map Introduction, Grouping Rules, Solved Examples

Karnaugh Map Introduction, Grouping Rules With Solved Examples 

 K-Map is a graphical illustration of a logic circuit in other words it is a graphical illustration of a truth table. 

Learning Objectives:

• Learn about Karnaugh Map, its grouping rules, cell adjacency rules

• Generate K-Map from the truth table

• Generate K-Map from a standard SOP/POS expression

• Generate K-Map from a non-standard SOP/POS expression

What is a K-Map?

It is a graphical method for simplifying Boolean expressions. It is a map containing boxes called "cells". The values in these cells represent a function in standard form (SOP or POS). For ‘n’ variables there are 2n cells. Each cell is denoted by a binary number or its equivalent decimal number. It is similar to the truth table in a way that both methods contain the output of a logic circuit for all possible input combinations. 

1. The truth table has rows and columns, each row has a different input combination. The K-Map has an array of cells, each cell is represented by a different combination of input variables.

2. With the help of the truth table, a standard SOP/POS expression is obtained. Each term in standard SOP/POS contains all the variables in the domain. The K-map is used for simplified SOP/POS expression. If applied properly, no need for further simplification.

3. The values entered in the truth table are curated in ascending order. The counting is in binary number format (not necessary but mostly it is in binary format). While in this method, values are curated in gray code format.

Understanding the principle of K-Map? How to develop a K-Map (Cell Adjacency rules):

Any two adjacent squares on the map differ by only a single variable. If a variable is primed in one cell, it is unprimed in the adjacent cell.

The two minterms are arranged in a way that there is a single variable change in binary numbers. When moving along any row or any column, one and only one variable changes in the product term. Look at the figure below:

How to construct a Karnaugh Map | K-Map?

There are many ways to describe a digital logic system.

• The logical expression

• The schematic

• The truth table 

• The Karnaugh Map

We can analyze the logic system easily if any of the above-mentioned entities is given. The K- Map can easily be implemented with the help of a logic expression either in standard or non-standard form. It is developed either with a schematic diagram or with the help of a truth table.

One Variable Map:

Consider a function with only one variable A. Since n = 1(number of variables), the number of possible cells in a map will be 2 (2n = 21 = 2). Each minterm is adjacent to only one minterm.

Two-Variable Maps

Consider a function with only one variable A and B. Since n = 2(number of variables), the number of possible cells in a map will be 4 (2n = 22 = 4). Each minterm is adjacent to two minterms.

Three Variable Maps

Consider a function with only one variable A, B and C. Since n = 3(number of variables), the number of possible cells in a map will be 8 (2n = 23 = 8). Each minterm is adjacent to three other minterms.

Four Variable Maps

Consider a function with only one variable A, B, C and D. Since n = 4(number of variables), the number of possible cells in a map will be 16 (2n = 24 = 16). Each minterm is adjacent to four other minterms.

Five Variable Maps

Consider a function with only one variable A, B, C, D and E. Since n = 5(number of variables), the number of possible cells in a map will be 2 (2n = 25 = 32). The 32 (4x8 map) cells map is quite large. Instead of a single larger map, it is constructed from two 4-variable K-Map. 

For cell adjacency, place a map on the top of the other.

Examples:

Example: F(A, B, C) = ∑ (0,2,3,7)

Have a look at group 1:

Variables A and C are non-changing while B changes. In one cell it is primed and in the other cell, it is unprimed. 

\[=\bar A \bar B \bar C + \bar A B \bar C\]

\[=\bar A \bar C (B + \bar B)\]

\[=\bar A \bar C\]

Look at group 2:

Variables B and C are non-changing, while A changes. In one cell it is primed and in the other cell, it is unprimed.

\[=\bar A B C +  A B C\]

\[=B C (A + \bar A)\]

\[=BC\]

Look at group 3:

Variables A and B are non-changing, while C changes. In one cell it is primed and in the other cell, it is unprimed.

\[=\bar A B \bar C + \bar A B C\]

\[=\bar A B(C + \bar C)\]

\[=\bar A B\]

\[F = \bar A \bar C+ B C +\bar AB\]

Example: F = \[\bar A \bar B \bar C + A \bar B \bar C + \bar A \bar B C + \bar A B  C \]

Two groups are formed, each group contains only two cells. The simplified expression contains only two SOP terms and each has two variables.

The simplified expression is

\[F = \bar B \bar C + \bar A C\]

Example: R = π (12, 13, 15)

This time a POS expression is given. It is obvious that mapping an SOP expression will give a non-simplified Boolean expression. 

Don't Care Condition:

In digital circuits, in some conditions, some input variables are not allowed. An example is the BCD codes. These codes are 0-9 (that is from binary 0000  to 1001). While the rest of the combinations are 10- 15 (that is from binary 1010 to 1111) are invalid. These input combinations will never occur.

In these situations simply draw the K-map according to the rules stated above. Mark the unwanted input combinations as 'don't care ('X')'. These terms or input combinations are termed as "don't care" conditions and marked as 'X' in K-map. These terms are advantageous while grouping. Add these 'X' and form larger groups. Larger groups result in simplified expressions. 

Example: \[F (A, B, C, D) =  ∑ (0,2,4,6,8)\]

\[d (A, B, C, D) = (10, 11, 12, 13, 14, 15)\]

Here we add some of them don't care terms to simplify the expression. While the rest of them are not included.

Example: \[F (W, X, Y, Z) = ∑ (1, 3, 7, 11, 15)\]

 \[F (W, X, Y, Z) = (0, 2, 5)\]