select the correct answer. which decimal number is equivalent to this binary number? 11111011\n\na. 31\nb…

select the correct answer. which decimal number is equivalent to this binary number? 11111011\n\na. 31\nb. 127\nc. 191\nd. 251

select the correct answer. which decimal number is equivalent to this binary number? 11111011\n\na. 31\nb. 127\nc. 191\nd. 251

Answer

Answer:

C. 191

Explanation:

Step1: Write the formula for binary - to - decimal conversion

[N=\sum_{i = 0}^{n - 1}a_{i}\times2^{i}] where (a_{i}) is the (i) - th digit of the binary number and (n) is the number of digits.

Step2: Identify the digits and their positions

For the binary number 11111011, from right - to - left: (a_0 = 1,a_1 = 1,a_2 = 0,a_3 = 1,a_4 = 1,a_5 = 1,a_6 = 1,a_7 = 1)

Step3: Calculate the decimal value

[ \begin{align*} N&=1\times2^{0}+1\times2^{1}+0\times2^{2}+1\times2^{3}+1\times2^{4}+1\times2^{5}+1\times2^{6}+1\times2^{7}\ &=1\times1 + 1\times2+0\times4 + 1\times8+1\times16+1\times32+1\times64+1\times128\ &=1 + 2+0 + 8+16+32+64+128\ &=191 \end{align*} ]