2nd October 2019
Why do we use hexadecimal numbers instead of binary numbers?
The main reason why we use hexadecimal numbers is because it is much easier to express binary number representations in hex than it is in any other base number system. Computers do not actually work in hex (don't laugh, beginning students do ask that question). Lets look at an example, using a byte.
Why is all data stored in binary form on a computer?
Binary is a mathematical number system: a way of counting. We have all learned to count using ten digits: 0-9. One probable reason is that we have ten fingers to represent numbers. The computer has switches to represent data and switches have only two states: ON and OFF.
The hexadecimal system is commonly used by programmers to describe locations in memory because it can represent every byte (i.e., eight bits) as two consecutive hexadecimal digits instead of the eight digits that would be required by binary (i.e., base 2) numbers and the three digits that would be required with decimal
Hexadecimal is the easiest way to write down binary numbers in a compact format. One important reason is because hex is ALOT shorter and easier to read than binary is for humans. Hexadecimal number is very easy to convert the numbers into binary, octal,and decimal system also.
The only rule you need to remember to convert from hexadecimal to binary is that one hexadecimal digit always poduces four binary digits. Because of this rule, there is a one to one relationship between a hexadecimal digit and a grouping of four binary digits.
The hexadecimal numeral system, also known as just hex, is a numeral system made up of 16 symbols (base 16). The standard numeral system is called decimal (base 10) and uses ten symbols: 0,1,2,3,4,5,6,7,8,9. Hexadecimal uses the decimal numbers and includes six extra symbols.
The hexadecimal numbers are 0-9 and then use the letters A-F. We show the equivalence of binary, decimal, and hexadecimal numbers in the table below. Hexadecimal is a convenient way to express binary numbers in modern computers in which a byte is almost always defined as containing eight binary digits.
- Divide the decimal number by 16. Treat the division as an integer division.
- Write down the remainder (in hexadecimal).
- Divide the result again by 16. Treat the division as an integer division.
- Repeat step 2 and 3 until result is 0.
- The hex value is the digit sequence of the remainders from the last to first.
A color hex code is a way of specifying color using hexadecimal values. The code itself is a hex triplet, which represents three separate values that specify the levels of the component colors. The code starts with a pound sign (#) and is followed by six hex values or three hex value pairs (for example, #AFD645).
Bitmap (or raster) images are stored as a series of tiny dots called pixels. Each pixel is actually a very small square that is assigned a color, and then arranged in a pattern to form the image. When you zoom in on a bitmap image you can see the individual pixels that make up that image.
Binary in Digital Computers and Electronic Devices. Numbers can be encoded in binary format and stored using switches. In a computer, switches are implemented using transistors. The smallest memory configuration is the bit, which can be implemented with one switch.
Of course, the internal machine representation of characters is in equivalent binary form. The ASCII table has 128 characters, with values from 0 through 127. Thus, 7 bits are sufficient to represent a character in ASCII; however, most computers typically reserve 1 byte, (8 bits), for an ASCII character.
DECIMAL NUMBERS IN BINARY
A binary code represents text, computer processor instructions, or any other data using a two-symbol system. The two-symbol system used is often the binary number system's 0 and 1. The binary code assigns a pattern of binary digits, also known as bits, to each character, instruction, etc.
In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit.
Denary, also known as "decimal" or "base 10," is the standard number system used around the world. It uses ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to represent all numbers. Denary is often contrasted with binary, the standard number system used by computers and other electronic devices.
An error that occurs when the computer attempts to handle a number that is too large for it. Every computer has a well-defined range of values that it can represent. If during execution of a program it arrives at a number outside this range, it will experience an overflow error.
Arithmetic operations have a potential to run into a condition known as overflow. When two signed 2's complement numbers are added, overflow is detected if: both operands are positive and the result is negative, or. both operands are negative and the result is positive.
In computer processors, the overflow flag (sometime called V flag) is usually a single bit in a system status register used to indicate when an arithmetic overflow has occurred in an operation, indicating that the signed two's-complement result would not fit in the number of bits used for the operation (the ALU width).
In computer processors the parity flag indicates if the number of set bits is odd or even in the binary representation of the result of the last operation. It is normally a single bit in a processor status register. For example, assume a machine where a set parity flag indicates even parity.