History of the Binary System - Cut-the-Knot

The table can be used to convert this decimal number to a binary number.

Binary System: history of invention, what it is, Euler's derivation

What I am going to show you today in binary is simply just the replacement of letters and numbers, with their binary equivalent. 1 and 0 are just a representation of on and off. 1 = on 0 = off. There are put in sections of "on and off's" also, usually sets of 8, called a byte. The digits are all valued exponentially, the easiest way to explain what that means is to show you, it is in the first picture at the bottom.

.To convert a decimal number to binary, you need only keep subtracting the largest power of two.

The Binary System - Technology Student

Besides hex is/was octal system used frequently too. It's disadvantage is that one octal digits describes a group of 3 bits only, not 4. as binary numbers in computers (for example, addresses) have often a range of a power of 2, the numbers fit better into groups of four than into groups of three.

To represent bigger whole numbers (integers), you need morebits -- more places in the binary number:

Adding two binary numbers together is like adding decimal numbers, except1 + 1 = 10 (in binary, that is), so you have to carry the one to the next column:

How to Convert from Decimal to Binary - wikiHow

The reduction of decimal to binary does increase the length of the number, a lot, but this is more than made up for in the increase in speed, memory and utilisation.

Binary numeral system - Wikipedia, the free encyclopedia

Therefore, the hex system isn't used by computers, but by humans, for terser representation of binary numbers, but easier convertibility than from/to decimal number system.

Binary System for Computers and Mathematics | …

Typical sizes for personal computer RAM (random access memory) are 4 to 16 megabytes, while hard disks now start around 150 megabytes. Since each byte can represent one character of the alphabet, that means a hard disk might hold something like 150 million characters, or25 million words of "raw" text. Documents formatted in a word processortake up a lot more space, though, and the operating system and software usually fill at least 100 megabytes.

Why is the binary system used? - Quora

The number system that you use is (since people have 10 fingers, this works out well for them). When you write the number 1853, for example it means:

The binary system is used for the same reason as the decimal ..

Computers don't use hex. There are no components in a computer working on hex values. Instead, computers work on binary values for most part, on digital "yes" and "no" information, represented as "voltage applied" and "no voltage", also called "hi" and "lo", or "1" and "0"

Meaning of binary number system

But what of the poor computer, which has no fingers to count on? Base 10 is not convenient for a fingerless computer to use. What computers DO have, are electrical circuits, which are either on or off. Just two states to work with. So the natural number system for use in an electronic computer is (called the number system). Unlike you who have ten digits to calculate with (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), the computer has only two digits (0 and 1) with which it must do everything. So, in a computer’s memory, a tiny transistor that is on (conducting a current) might represent a 1, while a transistor that is off would represent a 0 (zero).