Sure, let's convert the given binary number [tex]\(100000\)[/tex] to its decimal equivalent step-by-step.
1. Identify the Place Values in Binary:
Each digit in a binary number represents an increasing power of 2, starting from the rightmost digit (which represents [tex]\(2^0\)[/tex]).
For the binary number [tex]\(100000\)[/tex], it can be broken down as:
[tex]\[
1 2^5 + 0 2^4 + 0 2^3 + 0 2^2 + 0 2^1 + 0 2^0
\][/tex]
2. Calculate the Value of Each Binary Digit:
Let's calculate each term separately:
[tex]\[
1 2^5 = 1 32 = 32
\][/tex]
[tex]\[
0 2^4 = 0 16 = 0
\][/tex]
[tex]\[
0 2^3 = 0 8 = 0
\][/tex]
[tex]\[
0 2^2 = 0 4 = 0
\][/tex]
[tex]\[
0 2^1 = 0 2 = 0
\][/tex]
[tex]\[
0 2^0 = 0 1 = 0
\][/tex]
3. Sum the Results:
Now sum all the values obtained from the previous step:
[tex]\[
32 + 0 + 0 + 0 + 0 + 0 = 32
\][/tex]
So, the decimal equivalent of the binary number [tex]\(100000\)[/tex] is [tex]\(32\)[/tex].
