Question

convert 11111111 to decimal

Explanation:

Step1: Write binary - to - decimal formula

For a binary number \(a_{n}2^{n}+a_{n - 1}2^{n - 1}+\cdots+a_{1}2^{1}+a_{0}2^{0}\), where \(a_{i}\) is either 0 or 1. The binary number 11111111 can be written as \(1\times2^{7}+1\times2^{6}+1\times2^{5}+1\times2^{4}+1\times2^{3}+1\times2^{2}+1\times2^{1}+1\times2^{0}\).

Step2: Calculate each term

\(2^{7}=128\), \(2^{6} = 64\), \(2^{5}=32\), \(2^{4}=16\), \(2^{3}=8\), \(2^{2}=4\), \(2^{1}=2\), \(2^{0}=1\).

Step3: Sum up the terms

\(128 + 64+32 + 16+8+4+2 + 1=255\).

Answer:

255