Decimal is a Base 10 system with 10 possible values (0 to 9) and Binary is a Base 2 system with only two numbers 0 or 1.
i. Converting binary to decimal - The weightage of binary digits from right most bit position to the left most bit position is given below.
| 27 | 26 | 25 | 24 | 23 | 22 | 21 | 20 |
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Example: Convert 10011101 into a decimal value.
There are eight bits in the binary number. The decimal value for each bit position is given below:
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | « Decimal equivalent of the binary position |
| 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | « Given binary number |
To convert, you simply take a value from the top row wherever there is a 1 below, and then add the values together. For instance, in our example we would have
1*27 +
0*26 + 0*25 + 1*24 + 1*23 +
1*22 + 0*21 + 1*20
= 128 + 0 + 0 + 16 + 8 + 4 + 0+ 1
= 157 (decimal value)
ii. Converting decimal to binary
To convert decimal to binary is also very simple, you simply divide the decimal value by 2 and then write down the remainder, repeat this process until you cannot divide by 2 anymore.
For example, take the decimal value 157:
157 ÷ 2 = 78 with a remainder of 1
78 ÷ 2 = 39 with a remainder of 0
39 ÷ 2 = 19 with a remainder of 1
19 ÷ 2 = 9 with a remainder of 1
9 ÷ 2 = 4 with a remainder of 1
4 ÷ 2 = 2 with a remainder of 0
2 ÷ 2 = 1 with a remainder of 0
1 ÷ 2 = 0 with a remainder of 1 <--- to convert, write this remainder first
Next write down the value of the remainders from bottom to top (in other words write down the bottom remainder first and work your way up the list) which gives: 10011101 = 157
Example: What is the possible decimal equivalent of 10101010?
| Position of Bit | 7th | 6th | 5th | 4th | 3rd | 2nd | 1st | 0th |
| Decimal Value | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Calculate the decimal equivalent based on the above predefined values.
Given Binary Number is: 10101010, it's decimal equivalent is:
1*(2^7) + 0*(2^6) + 1*(2^5) + 0*(2^4) + 1*(2^3) + 0*(2^2) + 1*(2^1) + 0*(2^0)=170 in decimal format.
