Question

Translate each of the following binary representations into its equivalent base ten representation.

A. 1100
B. 10.011
C. 0.01
D. 10001

Answer 1

Answer:

12, 2.375, 0.25, 17

Explanation:

A. 2^3 + 2^2 = 12

B. 2^1 + 2^-2 + 2^-3 = 2.375

C. 2^-2 = 0.25

D. 2^4 + 2^0 = 17

Answer 2

Each of the binary numbers in the question have been translated to base ten to get the answers

• $1100_{two}=12_{ten}$
• $10.001_{two}=2.125_{ten}$

• $0.01_{two}=0.25_{ten}$

• $10001_{two}=17_{ten}$

We will make use of the following fact about binary numbers; each position has a value that is a power of two

$\text{... }\text{ }2^4\text{ }\text{ }2^3\text{ }\text{ }2^2\text{ }\text{ }2^1\text{ }\text{ }2^0\text{ }\text{ }.\text{ }\text{ }2^{-1}\text{ }\text{ }2^{-2}\text{ }\text{ }2^{-3}\text{ }\text{ ...}$

Any positions that are to the left of the point have powers of two that are greater or equal to 1. Positions to the right of the point have powers of two that are less than 1.

Converting the numbers to base ten (or decimal)

• Convert $1100_{two}$ to base ten

        $1100_{two}=1\times2^3+1\times2^2+0\times2^1+0\times2^0\\\\=8+4+0+0=12_{ten}$

• Convert $10.001_{two}$ to base ten

        $10.001_{two}=1\times2^1+0\times2^0+0\times2^{-1}+0\times2^{-2}+1\times2^{-3}\\\\=2+0+0+0+0.125=2.125_{ten}$

• Convert $0.01_{two}$ to base ten

        $0.01_{two}=0\times2^0+0\times2^{-1}+1\times2^{-2}\\\\=0+0+0.25=0.25_{ten}$

• Convert $10001_{two}$ to base ten

        $10001_{two}=1\times2^4+0\times2^3+0\times2^2+0\times2^1+1\times2^0\\\\=16+0+0+0+1=17_{ten}$

Learn more about converting from binary to decimal(base ten) here https://brainly.com/question/17946394