Question

Convert the following numbers from decimal to binary, assuming unsigned binary representation:________.

A) 35
B) 3
C) 27
D) 16

Answer 1

Binary representations of following are:

A) 35 = 100011

B) 3 = 11

C) 27 = 11011

D) 16 = 10000

Step-by-step explanation:

The method to generate the binary number from a decimal is :

Keep on dividing the number by 2 and keep on tracking the remainder

And the quotient is again divided and remainder is tracked so that the number is completely divided.

And then write the binary digits from bottom to top.

Please have a look at the method in below examples:

A) 35

`\begin{center}\begin{tabular}{ c c c }Number & Quotient & Remainder\\ 2 & 35 & 1 \\ 2 & 17 & 1 \\ 2 & 8 & 0 \\ 2 & 4 & 0 \\ 2 & 2 & 0 \\ 2 & 1 & 1\end{tabular}\end{center}`

Writing the remainder from bottom to top.

So, binary number is 100011

B) 3

`\begin{center}\begin{tabular}{ c c c }Number & Quotient & Remainder\\ 2 & 3 & 1 \\ 2 & 1 & 1 \\ \end{tabular}\end{center}`

Writing the remainder from bottom to top.

So, binary equivalent is 11.

C) 27

`\begin{center}\begin{tabular}{ c c c }Number & Quotient & Remainder\\ 2 & 27 & 1 \\ 2 & 13 & 1 \\ 2 & 6 & 0 \\ 2 & 3 & 1 \\ 2 & 1 & 1 \end{tabular}\end{center}`

Writing the remainder from bottom to top.

So, binary equivalent is 11011.

D) 16

`\begin{center}\begin{tabular}{ c c c }Number & Quotient & Remainder\\ 2 & 16 & 0 \\ 2 & 8 & 0 \\ 2 & 4 & 0 \\ 2 & 2 & 0 \\ 2 & 1 & 1 \\\end{tabular}\end{center}`

Writing the remainder from bottom to top.

So, binary equivalent is 10000.

Answers are:

Binary representations of following are:

A) 35 = 100011

B) 3 = 11

C) 27 = 11011

D) 16 = 10000