The short answer:
Digital electronics deals with 2 states, on and off. These states are represented with binary numbers. Hexidecimal is a shorthand for binary. It is earier to remeber the hex numbers because they are shorter.
The long answer:
In digital electronics signals are either hi or low. on or off. We choose to represent these as 1 for on/hi or 0 for low/off. A single signal is know as a bit and the number system using only 0's and 1's is binary.
Signals are often grouped together to convey more information or states. 4 bits is a nibble, 8 bits is a byte.
A nibble will have a binary value like 0b1100.
A byte will have binary value like 0b10101111.
Note the 0b tells us the number is in binary and the remainder of the numbers are binary digits or bits.
Binary numbers tend to be long. This makes them hard to work with. We could convert the binary numbers to base 10 but it is difficult to see the relationship between a decimal number and the value of each bit.
Hexidecimal is a better choice. A hex number start with 0x. The 0x is not part of the numbers value. It indicates the hex base.
The binary to hex mappings are:
0b0000 0x0
0b0001 0x1
0b0010 0x2
0b0011 0x3
0b0100 0x4
0b0101 0x5
0b0110 0x6
0b0111 0x7
0b1000 0x8
0b1001 0x9
0b1010 0xA
0b1011 0xB
0b1100 0xC
0b1101 0xD
0b1110 0xE
0b1111 0xF
Anyone who works with digital electronics need to memorize these 16 mappings. Once you have done so you can look at at multi digit hex number and know which bits are on and off.
When one looks at 0x0F one knows the binary value is 0b00001111. The binary value of 0x3C is 0b00111100. You do not need to think or use a culculator to do these conversions, you see the hex and know the binary.
Studens who learn these conversion will work faster and make fewer mistakes. I created a set of flash cards you can print to help learn the conversions between binary, hex, and decimal. Feel free to share them with you teacher and fellow students.
They can be found at: Microchip's **broken link removed**
Instructions for printing the flash cards.
Hexadecimal to Binary Flashcards
Hexadecimal to Decimal Flashcards
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