Numbers Representation Systems – Decimal, Binary, Octal and Hexadecimal

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If you store 8 electric signals, it can be interpreted as storing a binary number of 8 digits. Five low values followed by three high values can be interpreted as the binary number; Most people use the decimal numeral system or base ten. With one symbol we can represent the numbers zero to nine. If we represent ten, we use two symbols "10". When we want to represent a number from 99 towe use three symbols ",With one symbol we can represent number one and the zero.

To represent number two and threewe use two symbols. We have just seen that in decimal and binary numbers, they use 10 and 2 symbols respectively, to represent any number.

In computing, a bit is the smallest unit of information and can only take two values; zero or one. A bit, is a binary number of one digit.

A bit can be physically implemented with a two-state electronic device. A byte is made of 8 bits. It represents an 8-digit binary number. In a byte, we can store a number between and in the binary system, between 0 to in decimal system and between 00 to FF in hexadecimal system. When we talk about computer architecture, processors or operating systems, we understand that a word is a set of bits, usually 8, 16, 32 or 64 bits.

This means that most of the CPU registers are 32 bits, the information transfer unit is usually 32 bits, etc. Overall, we can think that the processor architecture is based on units of 32 bits. A bit operating system is ready to use a processor instruction set of bit. But it is also common that a bit CPU, can support bit instructions, so you can use a bit operating system.

Hexadecimal and binary numbers, byte, bit and word. Therefore, in programming, we often work with binary or hexadecimal numbers. Decimal Binary Hexadecimal 00 0 01 1 02 2 03 3 04 4 05 5 06 6 07 7 08 8 09 9 10 A 11 B 12 C 13 D 14 E 15 F. What is a computer?

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This is called the decimal number system and has base 10 , which means that this number system has 10 different digits to construct a number. But computers do not understand the decimal number system. Actually it's not their fault! We humans have created them that way! Unlike humans, the insides of computers know only 2 digits - 0 and 1 , because in the simplest electrical systems, electricity can only be "on" or "off.

All the numbers are constructed with only 2 digits - 0 and 1. A digit in binary that's a 0 or a 1 is also called a bit — which means bi nary digi t. Computers use this number system to add, subtract, multiply, divide and do all their other maths.

They even save data in the form of bits - well, they group them together into chunks of 8 bits. And don't forget, this chunk of 8 bits is called a byte. In normal maths, we don't use binary.

We were taught to use our normal number system. Binary is much easier to do math in than normal numbers because you only are using two symbols - 1 and 0 instead of ten symbols - 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

Computers use binary because they can only read and store an on or off charge. So, using 0 as "off" and 1 as "on," we can use numbers in electrical wiring.

Think of it as this - if you had one color for every math symbol 0 to 9 , you'd have ten colors. That's a lot of colors to memorize, but you have done it anyway. If you were limited to only black and white, you'd only have two colors.

It would be so much easier to memorize, but you would need to make a new way of writing down numbers. Binary is just that - a new way to record and use numbers which is true. In school, you were taught that we have a ones, tens, hundreds columns and so on they multiply by Binary also has columns, but they aren't ones and tens. The columns in binary are Binary is called base-2, because it uses two symbols.

So what makes binary so easy? The answer lies in how we read the number. If we had the number 52, we have a 2 in the ones column, adding 2 times 1 to the total 2. We have a 5 in the 10s column, multiply that together and get 50, adding that to the total.

Our total number is 52, like we expect. In binary, though, this is way simpler if you know how to read it fast. How do you write the number 3 from the base into a base-2 number?

What about the rest? Let's try writing the normal numbers from 1 to 10 in binary form, shall we? We said we'd write only the numbers from 1 to 10 into binary numbers, but look at that table!

It was so easy, we ended up converting the numbers until 16! But take note of how the binary numbers of 1, 2, 4, 8 and 16 match the previous table above. Have you noticed a pattern in writing binary numbers? Study the table for 1 to 16 again until you understand why in binary,. We have been trained to read these base numbers really quickly.

Reading binary for humans is slower since we are used to base You are now only just starting to learn how to read base-2, so it will be slow. You will get faster over time! We now have the number 52 as our total. The basics of reading a base-2 number is add each columns value to the total if there is a 1 in it.

You don't have to multiply like you do in base to get the total like the 5 in the tens column from the above base example , which can speed up your reading of base-2 numbers. Let's look at that in a table. The binary number is , but we don't know what it is. Let's go through the column-reading process to find out what the number is. We are done, so the total is the answer.

The answer is 11! Here are some more numbers for you to work out. Computers remember everything in binary. For example, if your name is "GEORGE" then the computer has some special binary word to store your name with only 0s and 1s.

This is just like using sign language. Every combination of gestures can mean a special word or number. Exactly in this manner, the computer has a different set of combinations for each letter or digit. A bit defines a binary dual state On or Off, 0 or 1, True or False which can not be broken into more smaller units. The name is short for binary digit, like the '1' in the binary number '10' representing decimal '2' in a similar fashion to how a decimal digit number that can have 10 distinct values in the default decimal base reference work, for instance the '9' and '8' that are part of the '98' decimal number.

A byte is eight bits put together or a group of 8 bits. It has to do with remembering letters, which you shall read later. From Wikibooks, open books for an open world.

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