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Computer number systems represent numbers inside the computer system architecture.
Every value saved or retrieved from the computer's memory uses a defined number system.
Understanding number systems aids in better comprehension of how computers perform calculations.
The true language of computers is the binary number system, operating in two states.
Digital computers represent data and information using binary numbers, which includes audio, graphics, video, text, and numbers.
The total count of digits in a number system equals its base, known as radix.
Computer architecture includes Binary, Octal, Decimal and Hexadecimal number systems.
Binary Number System
The term "binary" originates from "Bi-", which signifies two.
Only 0s and 1s are used in this system.
Letters, numbers, and other characters can all be represented.
Binary number's base is 2 due to its usage of just two digits.
A "bit" is a single binary number, serving as the fundamental unit for storing data in computer memory.
8 bits equals 1 byte.
1,024 bytes equal 1 kilobyte.
1,024 kilobytes equals 1 megabyte.
1,024 megabytes equals 1 gigabyte.
1,024 gigabytes equals 1 terabyte.
Conversion
In daily life, base 10, or the decimal number system, is commonly used.
Binary computation arose due to difficulties with decimal representation in computers.
Hexadecimal representation, which merges 4 binary bits, was created to simplify the longer binary numbers.
The octal representation simplifies by merging 3 binary bits.
Conversion should begin from right to left
Binary to Decimal Conversion
Follow these steps during conversion:
Expand the notation.
Write out position values.
Binary to Octal Conversion
The following steps should be done when preforming octal conversion:
Split the binary numbers into sets of 3 digits from the right.
Employ the expanded notation method.
Leading zeros must be added if needed.
Cancel the 0 if zero is the number in front.
Binary to Hexadecimal Conversion
Divide the binary numbers into sets of 4 digits from the right
Use the expanded notation method.
Any leading zeros must be added.
Cancel the 0 if zero is the number in front.
Decimal Number System
The decimal system is also called Hindu-Arabic or just Arabic
Includes the base 10.
Requires 10 unique numerals: the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Decimal Number Conversion
Division Quotient Remainder Method used
Division is preformed by 2
Copy the quotient to be divided again by 2.
If the numerator is less than the denominator, the quotient will automatically be 0 then just copy the numerator as the remainder.
Stop all operations when the quotient is already 0.
Conversion to Octal
Division Quotient Remainder Method is used
Division is permofed by 8
Copy the quotient to be divided again by 8
If the numerator is smaller than denominator the quotient is automatically 0. Then copy the numerator as the remainder
Operations stop when quotient is 0
Decimal to Hexadecimal conversion
Division Quotient Remainder Method
This is dcision by 16
Copy the quotient to divided again by 16
When numerator is less than denominator the quotient will automatically be zero. Copy the numerator as remainder
If quotient is already zero operations will stop
Octal Number System
Alternate name is "oct" and is the base-8 number system.
It uses the digits 0 to 7.
Octal numerals can be formed from binary numerals. This is done by grouping consecutive binary digits into groups of three starting from the right.
In computer programming, the octal equivalent of a binary number can be used to represent it because it occupies less space.
Octal Number Conversion
Steps for octal to binary conversion:
Separate he numbers, this conversion is the reverse of Binary to Octal
Get the last 3 digits
Leading zeros are added if needed
Octal to Decimal Conversion
With this conversion type the Expanded Notation Method
Like what the binary to decimal, use the expanded notation
Multiply by 8 starting from the right, going to the your left
Hexadecimal Number System
In mathematics and computing, hexadecimal (also base 16, or hex) is a positional numeral system with a radix, or base, of 16.
It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F (or alternatively a, b, c, d, e, f) to represent values ten to fifteen.
Hexadecimal Number Conversion
For hex to binary:
Separate the numbers
This conversion is the reverse of Binary to Hexadecimal
Get the last 4 digits
Add leading zeros if needed
When a 0 is in front, you may cancel it out
Hex to Decimal Conversion
With "hex to decimal" use the expanded notation
Use the expanded notation, but instead of multiplying it by 2, multiply it by 16
Start from the right going to your left