Shortcut for converting binary to decimal

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
 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 2starting from C0 to C7 respectively). The following table will give the exact idea how the values are obtained.

 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