Number Conversions & their Arithmetic

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Number Conversions & their Arithmetic June 24, 2019

There are more reasons why numbers are significant than one can count. In history, they were used to measure time, money, and dimensions.

But today, we use them in everything, not just in calculations but also for making predictions. Numbers provide us with various facilities that we utilize to organize everything. Time, Money, Weight, and most importantly, success and failures, maybe it is better to stop keeping track of them and focus on learning from your past differences.

Significance Of Numbers In Computers

Imagining a world without numbers would be chaotic. There will be no mathematics (I know that’s what most of us want), and people would have a hard time keeping things together. Everyone will start making assumptions instead of calculations and will drift away from accurate results, maybe 99.9 percent.

Text compare search in binary software

Binary Figures, Number Conversions & their Arithmetic

We have all heard about the term binary but do you know they are comprised of just two numbers 0 and 1? Additionally, these two numbers are utilized in calculating everything in a computer system. This is the format that computers put to use while performing every task. All the regular 0-9 numbers can be found in the base 10 number system, also known as the decimal system. Base 2 which are binary digits, only consists of two numbers which are used in mathematics and computer programming.

The binary number system was invented in the 17th century and was later used in machines for calculations.

This number system also lets us know if the current flows in a circuit, where 0 denotes no and 1 is yes. Computers today are made up of billions of transistors; they all act on the binary language because an operation is performed when it meets with the stored binary numbers in the computer.

Every character and bitmap pixels are made up of binary digits. That means they are stored as a sequence of numbers in the memory. Also, if you increase the color depth of a bitmap graphic, you will find a significant difference in the size of the file.

The data that we enter in computers, for example, numbers or alphabets, they are all assigned unique eight-digit binary numbers. So, when you press a letter, the network doesn’t know that it is an alphabet, it only knows that it is a large eight-digit binary number.

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Let’s keep things simple:

At an early age, we were taught a number system which is known as decimal, and if you remember we were also instructed on how to calculate positional values like tens, hundreds, thousands, etc. The only thing that was missing at the time was the rule in which we calculate these values. As number systems start with one’s position, the digit left to the first number will be one times the base, for example, the number on the left of the first will be 1×10 means tens, on the second place the amount will be 1×100 that marks it hundreds and so on. In decimal, the numbers mount up to 9 starting from 0.

Binary arithmetic includes

  • Division,
  • Multiplication,
  • Addition,
  • and subtraction.

The method to add binary numbers is simple 0+1, 1+0 will equal to one where 0+0 and 1+1 will equal to zero and one (by adding the amount to next bit) the same goes for 1-1 which is equal to one and will borrow from the other bit. The method of multiplication, however, is the same used in mathematics without adding or acquiring numbers from other bits. For example, 1×1 will be one, and the rest, when multiplied by zero, will remain zero.