Conversion Between Binary and Decimal - JSS2 Computer Studies Lesson Note
Decimal to Binary:
To convert a decimal number to binary, you repeatedly divide the decimal number by 2 and record the remainders. The binary equivalent is read from the bottom to the top, taking the remainders in reverse order.
For instance, to convert decimal 14 to binary:
14÷2=7(remainder 0)
7÷2=3(remainder 1)
3÷2=1(remainder 1)
1÷2=0(remainder 1)
Reading the remainders in reverse order, the binary representation of 14 is "1110."
Binary to Decimal:
To convert a binary number to decimal, you multiply each binary digit by the corresponding power of 2 and sum the results.
For example, the binary number "1011" is calculated as: 1×23+0×22+1×21+1×20=8+0+2+1=11
In conclusion, the binary system is the backbone of digital data representation in computers, using only 0s and 1s to convey information. Understanding how to convert between binary and decimal is crucial for grasping the core principles of computer science. The simplicity and elegance of the binary system form the basis for complex operations in computer programming, data storage, and digital communication.