Question

In 100 words or less describe how place value is used in the binary number system. How is it similar or different from the way place value is used in the base 10 number system.

Answer 1

See explanation

Explanation:

The place value for the binary system has a base of 2.

Let us create a place value chart in base 2 up to 5 bits

`\begin{center}\begin{tabular} c 2^4& 2^3& 2^2&2^1&2^0\\16 & 8& 4 &2&1\\ sixteens place &Eights place&Fours place&twos place&ones place\end{tabular}\end{center}`

So in the binary system, the pace values are ones, twos, fours,...fourths, eighths, etc while the decimal system we have ones,tens, hundreds,...,tenths, hundredths, etc

For the binary system we have up to only 2 bits, that is 0s and 1s unlike the decimal system where have 0,1,2,3,4,5,6,7,8,9

Therefore the place value of 0 in 1011 in binary system is fours while the place value of 0 in 1011 in decimal system is hundreds.

When we are subtracting decimal system, "borrowing" from each digit has a value of 10 whereas in the binary system "borrowing" from each digit has a value of 2

In binary system, we move in powers of 2 while in the decimal system we move in the powers of 10.