Why Hexadecimal for Computers?

Question

What base does it use? Please explain the relationship between Binary and Hexadecimal. Show how "A0D3" this hexadecimal number is represented in both binary and base10. Please include an explanation.

I'm just curious.

Answer 1

Binary is raw language/data of a computer, it is base 2. Hexadecimal is base 16.

It is easier to convert Binary to Hex and vice-verse compared to standard numbers (base 10). By grouping Binary numbers by 4, you can actually convert it directly to Hex, and vice versa. Below is a table of the conversion:

0 = 0000
1 = 0001
2 = 0010
3 = 0011
4 = 0100
5 = 0101
6 = 0110
7 = 0111
8 = 1000
9 = 1001
A = 1010
B = 1011
C = 1100
D = 1101
E = 1110
F = 1111

In short A0D3 (using the above table) converts to binary as 1010 0000 1101 0011

So if you write something like 1101001010010001, and group it by four 1101 0010 1001 0001 mean D291.

With base 10, you will need to compute it manually (for A0D3 see below)

A = 10 * 16^3 (or 10 * 16 * 16 * 16) = 40960
0 = 0 * 16^2 (or 0 * 16 * 16) = 0
D = 13 * 16^1 (or 13 * 16) = 208
3 = 3 * 16^0 (or 3 * 1) = 3

then you have to add the results which is 41171.

Answer 2

Hex is base 16

Regardless of using hex or base10 system, hardware wise, a computer only handles binary numbers, so that's the relationship binary number has with all other number system that you use in programming

in binary, it takes 4 bits to represent a hexa digit. In normal number system, you have to represent it digit by digit, you cannot represent 35 as in 35, but rather, represent it as 3 and 5.

3 bits can represent 8 digits only, not 10 that is required in 0-9. 4 bits represent 16 different digit, 0-9,A,B,C,D,E,F.

base10 falls between 3 and 4 bits, 4 bits is a waste since it can represent 16 different digit, so use hexa in low level programming, as it's easier rather than having the programmner program in strings of bits. represent thing hex of 1111 in binary will be 0001000100010001.... see how long binary is.

Answer 3

Pertaining to a number system that has just two unique digits. For most purposes, we use the decimal number system, which has ten unique digits, 0 through 9. All other numbers are then formed by combining these ten digits. Computers are based on the binary numbering system, which consists of just two unique numbers, 0 and 1. All operations that are possible in the decimal system (addition, subtraction, multiplication, division) are equally possible in the binary system.
We use the decimal system in everyday life because it seems more natural (we have ten fingers and ten toes). For the computer, the binary system is more natural because of its electrical nature (charged versus uncharged).

In the decimal system, each digit position represents a value of 10 to the position's power. For example, the number 345 means:

3 three 100s (10 to the 2nd power)

plus

4 four 10s (10 to the first power)

plus

5 five 1s (10 to the zeroth power)

In the binary system, each digit position represents a value of 2. For example, the binary number 1011 equals:

1 one 8 (2 to the 3rd power)

plus

0 zero 4s (2 to the 2nd power)

plus

1 one 2 (2 to the first power)

plus

1 one 1 (2 to the zeroth power)

So a binary 1011 equals a decimal 11.

Because computers use the binary number system, powers of 2 play an important role. This is why everything in computers seems to come in 8s (2 to the 3rd power), 64s (2 to the 6th power), 128s (2 to the 7th power), and 256s (2 to the 8th power).

Programmers also use the octal (8 numbers) and hexadecimal (16 numbers) number systems because they map nicely onto the binary system. Each octal digit represents exactly three binary digits, and each hexadecimal digit represents four binary digits.

Answer 4

Hexadecimal For

Answer 5

Hex is base 16 and one hexadecimal digit is four binary digits.

The number A0D3 can be broken down into binary by its individual parts as:
A = 1010
0 = 0000
D = 1101
3 = 0011

Put together, they make the number 1010000011010011 which is 41171 in decimal (base-10).

Answer 6

ok this is how it works: binary is used to store\transfer\transmit\Prosess data to and from the user. Hex is used to represent it, and more sepecifically used by engineers in embedded coding\programing. relation ship i will give with an example.for an 8 bit processor(computer) your data A0D3 will be written\stored by your processor as

1010 0000 1101 0011
A 0 D 3
This scheme is easier to write codes and debug codes. you have to play with just 4 characters A0D3 in hex rather than 16 caharcters in binary, which is confusing and time consuming. now comes decimal. we use that in our daily life so we convert hex\binary to decimal so that the end user can understand it. so A0D3 will be 41171.know that decimal format is base10, hex is base 16 and binary is base2. for more details on number formats refer the links below.
If you have any doubts mail me. even if you dont get the reply soon dont worry i will reply it to you one i check my mail.
I hope this clears your doubt. on how to convert them you need to again ask me if you really need it.

Answer 7

base 16 and base 2 are easily convertible
computer actually uses base 2 but due to easier representation base 16 is used
A0D3=1010000011010011=41171