Binary to Decimal conversion
How to convert binary to decimal
For binary number with n digits:
dn-1 … d3 d2 d1 d0
The decimal number is equal to the sum of binary digits (dn) times their power of 2 (2n):
decimal = d0×20 + d1×21 + d2×22 + …
Example:1
Find the decimal value of 11001:
Convert (11001)2 to (n)10
| binary number: | 1 | 1 | 0 | 0 | 1 |
| power of 2: | 24 | 23 | 22 | 21 | 20 |
=> 1*24 + 1*23 + 0*22 + 0*21 + 1*20
=> 16 + 8 + 0 + 0 + 1
=> 25
So we have
(11001)2 = (25)10
Example:2
Find the decimal value of 1101:
Convert (1101)2 to (n)10
| Binary Number | 1 | 1 | 0 | 1 |
| Power of 2 | 23 | 22 | 21 | 20 |
=> 1*23 + 1*22 + 0*21 + 1*20
=> 8 + 4 + 0 + 1
=> 13
So we have
(1101)2 = (13)10
Example:3
Find the decimal value of 10011:
Convert (10011)2 to (n)10
| Binary Number | 1 | 0 | 0 | 1 | 1 |
| Power of 2 | 24 | 23 | 22 | 21 | 20 |
=> 1*24 + 0*23 + 0*22 + 1*21 + 1*20
=> 16 + 0 + 0 + 2 + 1
=> 19
So we have
(10011)2 = (19)10
