Maximum Decimal Number Representable with 10 Binary Digits

Binary digits, commonly known as bits, are the smallest unit of information used in computing and digital communications. They can only represent two states, 0 or 1, making binary a base-2 numeral system. In contrast, decimal is a base-10 numeral system that can represent ten states, 0 through 9.

Conversion from Binary to Decimal

To convert a binary number to a decimal number, each binary digit is multiplied by 2 raised to the power of its position, starting from the rightmost digit. The resulting products are then added together to get the decimal equivalent.

Calculation of Maximum Decimal Number

With 10 binary digits, the largest binary number that can be represented is 1111111111. To calculate its decimal equivalent, we use the conversion formula:

1 x 2^9 + 1 x 2^8 + 1 x 2^7 + 1 x 2^6 + 1 x 2^5 + 1 x 2^4 + 1 x 2^3 + 1 x 2^2 + 1 x 2^1 + 1 x 2^0

= 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1

= 1023

Therefore, the maximum decimal number that can be represented with 10 binary digits is 1023.

Conclusion

In summary, binary digits can only represent two states, 0 or 1, making binary a base-2 numeral system. To convert binary to decimal, each binary digit is multiplied by 2 raised to the power of its position. With 10 binary digits, the maximum decimal number that can be represented is 1023.

Number will have 10 bits,wherein each bit can be 0 or 1.To generate maximum number we place 1 at every index position.

Which when converted to decimal is 1023.

(2^10-1)






App isn't accepting 1's together in a line so please understand the first line.