We have till now discussed the conventional method of converting binary numbers to decimal numbers. Instead, of following the long procedure here you will learn a simple shortcut to perform the conversions in matter of seconds and as you practice you will be able to mentally convert binary number to decimal without the pen and the paper.
However, the earlier procedure is a must in examination point of view. This shortcut is only for knowledge and fun.
Step 1: First, we will have to make a tabular column with three rows R1,R2,R3 and 8 columns C0,C1,C2,C3,C4,C5,C6,C7 as shown below
C7 C6 C5 C4 C3 C2 C1 C0
| R1 | ||||||||
| R2 | ||||||||
| R3 |
Here, each element of the table will hold one bit and there are 8 columns which means 8 bits in one row (i.e. 1 byte). In this shortcut the maximum value that we cover is (255) in decimal number system and you can extend it if you wish.
Step 2: Now insert the values into the first row of the table (R1) as shown below
C7 C6 C5 C4 C3 C2 C1 C0
C7 C6 C5 C4 C3 C2 C1 C0
| R1 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| R2 | ||||||||
| R3 |
You would be wondering from where did those values in the first row come from. It is simply the values of powers of 2 ranging from (20 to 27 starting from C0 to C7 respectively). The following table will give the exact idea how the values are obtained.
Step 3 : The given binary number that needs to be converted to decimal is inserted bit by bit from LSB to MSB into third row (R2) starting from C0 to C7 respectively.
Step 4: Multiply each element from the first row (R1) with the corresponding value in the second row (R2) and put the product into the third row (R3) in the same column.
Step 5: Now add the individual columns of third row and the sum gives the decimal equivalent of the binary number.
Lets get started with solving some simple examples that will help you a better picture about the shortcut. As we proceed with more examples we will reduce the number of steps.
Example 1: Convert ( 1001 )2 to ( ? )10
step 1: Draw the tabular column with the values
C7 C6 C5 C4 C3 C2 C1 C0
| Binary | Decimal |
| 20 | 1 |
| 21 | 2 |
| 22 | 4 |
| 23 | 8 |
| 24 | 16 |
| 25 | 32 |
| 26 | 64 |
| 27 | 128 |
Step 3 : The given binary number that needs to be converted to decimal is inserted bit by bit from LSB to MSB into third row (R2) starting from C0 to C7 respectively.
Step 4: Multiply each element from the first row (R1) with the corresponding value in the second row (R2) and put the product into the third row (R3) in the same column.
Step 5: Now add the individual columns of third row and the sum gives the decimal equivalent of the binary number.
Lets get started with solving some simple examples that will help you a better picture about the shortcut. As we proceed with more examples we will reduce the number of steps.
Example 1: Convert ( 1001 )2 to ( ? )10
step 1: Draw the tabular column with the values
C7 C6 C5 C4 C3 C2 C1 C0
| R1 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| R2 | ||||||||
| R3 |
Step 2: Insert given binary number into 2nd row as stated in step 3
C7 C6 C5 C4 C3 C2 C1 C0
| R1 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| R2 | 1 | 0 | 0 | 1 | ||||
| R3 |
The empty columns can be ignored
Step 3: Multiply R1 and R2 with the corresponding elements and put the product in R3
C7 C6 C5 C4 C3 C2 C1 C0
| R1 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| R2 | 1 | 0 | 0 | 1 | ||||
| R3 | 8 | 0 | 0 | 1 |
Step 4: Now add the individual elements of third row R3, this sum gives the decimal equivalent of the given binary number as illustrated
8 + 0 + 0 + 1 = ( 9 )10
Example 2 : ( 1 0 1)2 = ( ? )10
C7 C6 C5 C4 C3 C2 C1 C0
| R1 | 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| R2 | 1 | 0 | 1 | |||||
| R3 | 4 | 0 | 1 |
4 +0 + 1 = ( 5 )10
Try the following yourself
Example 3: (101010)2= ( ? )10
Example 4: (111111)2= ( ? )10
Example 5: (00011)2= ( ? )10
Example 6: (10)2= ( ? )10