Translate decimal to binary. Translating binary to decimal.
How to translate binary to decimal manually?
The binary number system, or base 2, represents values with two chars, 0 and 1. Each digit is based on a power of number 2.
We can use the table below to convert binary into decimal and decimal to binary. If the binary number is equal to 1  the digit is "true", if it is 0  the digit is "false". You do not need to write seven zeros to represent the binary value of 1, 00000001 is equal to 1 and 00100100 is equal to 00100100 or 36 in decimal.
2^{7}=128  2^{6}=64  2^{5}=32  2^{4}=16  2^{3}=8  2^{2}=4  2^{1}=2  2^{0}=1 
128  64  32  16  8  4  2  1 
1  0  1  1  1  0  0  1 
Example.
Decimal value of 10111001 will be a resulting sum of "true" bits. 128 + 32 + 16 + 8 + 1 = 185.
To convert 10111001 back into decimal value, we must start by dividing 185 by first possible value that is lower than 185.
185 / 128 = 1, 185  128 = 57. Now we can divide 57 by 32, 57 / 32 = 1, 57  32 = 25. 25 / 16 = 1, 25  16 = 9. 9 / 8 = 1, 9  8 = 1. 1 / 1 = 1.
Now we got 128 = 1, 32 = 1, 16 = 1, 8 = 1, 1 = 1. But 64 = 0, 4 = 0 and 2 = 0.
If you put these values back into the table, you will get 10111001.
