A Binary Number 1100011 Has The Decimal Value Equal To _____?

A binary number 1100011 has the decimal value equal to _____?

Explanation

To convert the binary number $11000 111$ to decimal:

Write down the binary number: $11000 111$
Identify each bit's position from right to left: $2^{0}, 2^{1}, 2^{2}, 2^{3}, 2^{4}, 2^{5}, 2^{6}$
Assign the binary digits to their respective positions: $1, 1, 0, 0, 0, 1, 1$

Now, calculate the decimal value:

$1 \times 2^{6} + 1 \times 2^{5} + 0 \times 2^{4} + 0 \times 2^{3} + 0 \times 2^{2} + 1 \times 2^{1} + 1 \times 2^{0}$

$= 64 + 32 + 0 + 0 + 0 + 2 + 1$

$= 99$

So, the decimal value of $11000 111$ is $99$

Therefore, the correct answer for the MCQ would be:

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Explanation

Let numbers be $n, n + 1, n + 2, n + 3$
Product= $n(n+1)(n+2)(n+3)$
Add 1 → expression becomes a perfect square.

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