Calculating Binary Number
December 15, 2008
Binary works on “base two” which contains the of digit of 1 and 0. “Base Ten” is 0-9 which we use every day.
Base 2 = Binary = 01 (2 digits)
Base 10 = 0123456789 (9 digits)
Binary uses the exponential form of 2 like 2^0, 2^1, 2^2…. Also binary works from right to left instead of our regular left to right that we read with.
Base Two
2^0=1, 2^1=2, 2^2=4, 2^3=8, 2^4=16, 2^5=32, 2^6=64, 2^7=128, 2^8=256
|
2^7 |
2^6 |
2^5 |
2^4 |
2^3 |
2^2 |
2^1 |
2^0 |
|
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
Each base is 1 bit, and 8 bits like the table above equals to 1 byte.
1024 bytes are 1 kilo byte.
|
1 bit |
|
|
8 bits |
1 byte |
|
1024 B |
1 kilobyte |
|
1024 kB |
1 Megabyte |
|
1024 mB |
1 Gigabyte |
|
1024 GB |
1 Terabyte |
|
1024 TB |
1 Petabyte |
To use Binary numbers, you need to convert it to Base 10
|
2^7 |
2^6 |
2^5 |
2^4 |
2^3 |
2^2 |
2^1 |
2^0 |
Base 10 # |
|
128 |
64 |
32 |
16 |
8 |
4 |
2 |
1 |
|
|
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
|
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
3 |
|
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
7 |
|
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
15 |
|
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
31 |
|
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
63 |
|
0 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
127 |
|
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
255 |
By using the table above, you can convert base 2 to base 10 and base 10 to base 2. To convert base 10 to base 2, just convert the base 2 digits until it equals the base 10 number.
