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Number Systems & Conversions, | 128 | 64 | 32 …
Number Systems & Conversions
Binary
Converting to binary and denary is simple. This is generally done in 8 bits. A table is used with 8 columns for each bit. The far right most is 1 and each column is the previous times 2.
Hexadecimal
Hexadecimal works like this
0 | 0
1 | 1
2 | 2
3 | 3
4 | 4
5 | 5
6 | 6
7 | 7
8 | 8
9 | 9
10 | A
11 | B
12 | C
13 | D
14 | E
15 | F
There are 16 digits in total. 0-15 in denary and 0 - F in hexadecimal.
Hexadecimal works similar to binary
The rightmost digit is the number of 1s. The one to the left of that is the number of 16's. The one to the left of that is the number of 256s (16*16) etc
16s | 1s
0 | A
Hex 0A represents denary 10 because ((0×16)+(1×10))=10
16s | 1s
3 | 0
Hex 30 represents denary 48 because ((3×16)+(0×1))=48
16s | 1s
A | A
Hex AA represents 170 because ((10×16)+(1×10))=170
Number systems
Hexadecimal is a base 16 system
Denary is a base 10 system
Binary is a base 2 system
Conversion between Hex and Binary
If I want to convert from Hex BA to binary then I can do this by working out the binary digits for each and then joining those nibbles together
Converting from Hex BA to binary
Hex B (denary 11)
8 | 4 | 2 | 1
1 | 0 | 1 | 1
When joining these two together, they make 10111010
Hex A (denary 10)
8 | 4 | 2 | 1
1 | 0 | 1 | 0
10111010 can be proved correct
128 | 46 | 32 | 16 | 8 | 4 | 2 | 1
1 | 0 | 1 | 1 | 1 | 0 | 1 | 0
This binary adds to 186 (128 + 32 + 16 + 8 + 2)
Both the binary results and the hex results are the same so this proves that it is correct
BA is the original hex
That's B × 16 (11×16) = 176
Plus A × 1 (10×1) = 10
176 + 10 = 186
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
By setting each on of these numbers to either a one or zero, you can represent different numbers.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
10000000 represents 128 because only one of the columns is activated which is the 128 column.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 |
00101000 represents 40 because the 32 and 8 columns are activated which add up to 40.
Decimal/Denary | Hexadecimal
Hex table
How it works
Examples