Convert the following binary numbers to decimal.
a) 10100 b) 110110
The correct answer and explanation is:
Let’s convert the binary numbers into decimal.
a) Binary number: 10100
To convert a binary number to decimal, we multiply each digit of the binary number by 2 raised to the power of its position, starting from 0 on the rightmost side.
For 10100:
- The rightmost digit is at position 0, the next at position 1, and so on.
- We multiply each binary digit (0 or 1) by 2 raised to the power of its position:
1×24=161 \times 2^4 = 16 0×23=00 \times 2^3 = 0 1×22=41 \times 2^2 = 4 0×21=00 \times 2^1 = 0 0×20=00 \times 2^0 = 0
Now, add all the results together: 16+0+4+0+0=2016 + 0 + 4 + 0 + 0 = 20
So, the decimal equivalent of 10100 is 20.
b) Binary number: 110110
For 110110:
- Similarly, each digit is multiplied by 2 raised to the power of its position, starting from the rightmost digit.
1×25=321 \times 2^5 = 32 1×24=161 \times 2^4 = 16 0×23=00 \times 2^3 = 0 1×22=41 \times 2^2 = 4 1×21=21 \times 2^1 = 2 0×20=00 \times 2^0 = 0
Now, add all the results together: 32+16+0+4+2+0=5432 + 16 + 0 + 4 + 2 + 0 = 54
So, the decimal equivalent of 110110 is 54.
Summary:
- a) The decimal equivalent of 10100 is 20.
- b) The decimal equivalent of 110110 is 54.
This method is based on the binary number system, where each place value is a power of 2, starting from 202^0 on the rightmost side.