What is the largest decimal number representable with eleven binary bits?

To determine the largest decimal number representable with eleven binary bits, it's important to understand how binary numbering works.

A binary bit can represent two states: 0 or 1. Therefore, the total number of distinct values that can be represented by ( n ) bits is ( 2^n ). In the case of eleven bits, you can represent ( 2^{11} ) different combinations. However, the range of values that can be represented starts from 0 to a maximum value.

The maximum value occurs when all bits are set to 1. For eleven bits, this would be:

• If you have eleven bits, the maximum value in binary is ( 11111111111_2 ).

To convert this binary number to decimal, you can use the formula for converting binary to decimal:

[

\text{Decimal Value} = 1 \times 2^{10} + 1 \times 2^{9} + 1 \times 2^{8} + 1 \times 2^{7} + 1 \times 2^{6} + 1 \times 2^{5} + 1 \times 2^{4} + 1 \times