1. Binary Positional Notation
Since we as humans use the decimal number system it is often necessary for us to convert binary numbers into their corresponding decimal number. For example, what does the binary number 1010 equal in decimal? Press next to find out how positional notation is used to determine the answer.

2. Step 1 : Determine place values by using increasing powers of 2.16 8 4 2 1 24 23 22 21 20
Place Value
Power

3. Step 2 : Write the binary number’s digits (1010)
under the corresponding place values. 16 8 4 2 1 24 23 22 21 20
Place Value
Power
Numerals

4. Step 3 : Multiply each numeral by its corresponding place value16 8 4 2 1 24 23 22 21 20
Place Value
Power
Numerals
0 * 1 =

5. 16 8 4 2 1 24 23 22 21 20
Place Value
Power
Numerals
0 * 1 =
1 * 2 =

6. 16 8 4 2 1 24 23 22 21 20
Place Value
Power
Numerals
0 * 1 =
1 * 2 =
0 * 4 =

7. 16 8 4 2 1 24 23 22 21 20
Place Value
Power
Numerals
0 * 1 =
1 * 2 =
0 * 4 =
1 * 8 =

8. 16 8 4 2 1 24 23 22 21 20
Place Value
Power
Numerals
0 * 1 =
1 * 2 =
0 * 4 =
1 * 8 =
0 * 16 =

9. Step 4 : Add products together16 8 4 2 1 24 23 22 21 20
Place Value
Power
Numerals
0 * 1 =
1 * 2 =
0 * 4 =
1 * 8 =
0 * 16 = + 10
Therefore the binary number 1010 is equal to 10 in decimal.