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Title: Binary, Denary and Hexadecimal
Description: Here are some Computer Science/Studies on binary, denary and hexadecimal. These notes help you understand binary, denary and hexadecimal; it also guides you on what they all represent (number-wise) and how you can convert them from each other. It also describes and explains what binary, denary and hexadecimal are used for.
Description: Here are some Computer Science/Studies on binary, denary and hexadecimal. These notes help you understand binary, denary and hexadecimal; it also guides you on what they all represent (number-wise) and how you can convert them from each other. It also describes and explains what binary, denary and hexadecimal are used for.
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Binary
Smallest to largest:
Bit – 1 piece of data
Nibble – 4 pieces of data
Byte – 8 pieces of data
Kilobyte – 1024 pieces of data
Megabyte – 1024 Kilobytes
Gigabyte – 1024 Megabytes
Terabyte – 1024 Gigabytes
One bit can store two values (0 and 1)
...
Two bits give us four values
...
The number system we use is called DENARY or DECIMIL
...
Denary
2
X1000
4
2
x100
4
x10
2 thousand 4 hundred and twenty-four
2x1000 + 4x100 + 2x10 + 4x1
x1
8
4
2
1
0
1
0
1
IS 5 IN DENARY
8x0 + 4x1 + 2x0 + 1x1 = 5
1
1101
- 1 DIGIT = 1 BIT
- 4 DIGITS = A NIBBLE
11011001 -8 DIGITS = A BYTE
8
4
2
1
1
1
1
1
= 15
0
1
1
0
=6
1
0
0
1
=9
1
1
0
1
= 13
1
0
1
1
= 11
0
0
0
1
=1
1
0
0
0
=8
Hexadecimal
Hexadecimal is Base 16
We need binary because computers work on the principle of 2 states,
that something is either ON/TRUE or OFF/FALSE, this can only be done
with base 2 (binary) and if it was done with decimal/base 10 there would
be 10 different states!
Problems with binary:
Numbers can become very long
...
Hexadecimal (a shortcut to binary)
4096
256
16
1
0
1
2
3
Hexadecimal is Base 16
...
(1x256) + (2x16) + (3x1) = 291
Denary
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Hexadecimal
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F
To convert Binary numbers to hex:
10110110
Split the number into separate nibbles:
1011
0110
Then convert each nibble to denary:
11
6
Then convert each denary number to hex:
B
6
Why are Hexadecimal numbers used?
Hexadecimal numbers are better remembered than long binary
numbers
...
How to convert denary to hexadecimal:
Convert the denary number 45 into a hex number
...
It may be easier to go via denary to get a
binary number
...
Denary looks like a
regular number but it just represents binary code
...
We multiply all the numbers by what they represent: 8x1, 4x0, 2x1,
1x1
...
2
...
Adding the
numbers are a bit harder than the multiplying
...
You have your answer; in our case, 11
...
Since the first number is a 0, we can exclude that
...
64x1, 32x0, 16x1, 8x1, 4x1, 2x0, 1x1
3
...
Add the remaining numbers: 64 + 16 + 8 + 4 + 2 + 1 = 95
5
...
Title: Binary, Denary and Hexadecimal
Description: Here are some Computer Science/Studies on binary, denary and hexadecimal. These notes help you understand binary, denary and hexadecimal; it also guides you on what they all represent (number-wise) and how you can convert them from each other. It also describes and explains what binary, denary and hexadecimal are used for.
Description: Here are some Computer Science/Studies on binary, denary and hexadecimal. These notes help you understand binary, denary and hexadecimal; it also guides you on what they all represent (number-wise) and how you can convert them from each other. It also describes and explains what binary, denary and hexadecimal are used for.