analog signal

[logistic_guy]

Consider a \(\displaystyle 4\)-bit digital word \(\displaystyle D = b_3b_2b_1b_0\) (see Eq. \(\displaystyle 1.3\)) used to represent an analog signal \(\displaystyle v_A\) that varies between \(\displaystyle 0 \ \text{V}\) and \(\displaystyle +15 \ \text{V}\).

\(\displaystyle \bold{(a)}\) Give \(\displaystyle D\) corresponding to \(\displaystyle v_A = 0 \ \text{V}, 1 \ \text{V}, 2 \ \text{V},\) and \(\displaystyle 15 \ \text{V}\).
\(\displaystyle \bold{(b)}\) What change in \(\displaystyle v_A\) causes a change from \(\displaystyle 0\) to \(\displaystyle 1\) in \(\displaystyle (\text{i}) \ b_0, (\text{ii}) \ b_1, (\text{iii}) \ b_2,\) and \(\displaystyle (\text{iv}) \ b_3\)?
\(\displaystyle \bold{(c)}\) If \(\displaystyle v_A = 5.2 \ \text{V}\), what do you expect \(\displaystyle D\) to be? What is the resulting error in representation?

 

[khansaheb]

Consider a \(\displaystyle 4\)-bit digital word \(\displaystyle D = b_3b_2b_1b_0\) (see Eq. \(\displaystyle 1.3\)) used to represent an analog signal \(\displaystyle v_A\) that varies between \(\displaystyle 0 \ \text{V}\) and \(\displaystyle +15 \ \text{V}\).

\(\displaystyle \bold{(a)}\) Give \(\displaystyle D\) corresponding to \(\displaystyle v_A = 0 \ \text{V}, 1 \ \text{V}, 2 \ \text{V},\) and \(\displaystyle 15 \ \text{V}\).
\(\displaystyle \bold{(b)}\) What change in \(\displaystyle v_A\) causes a change from \(\displaystyle 0\) to \(\displaystyle 1\) in \(\displaystyle (\text{i}) \ b_0, (\text{ii}) \ b_1, (\text{iii}) \ b_2,\) and \(\displaystyle (\text{iv}) \ b_3\)?
\(\displaystyle \bold{(c)}\) If \(\displaystyle v_A = 5.2 \ \text{V}\), what do you expect \(\displaystyle D\) to be? What is the resulting error in representation?

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[logistic_guy]

Eq. \(\displaystyle 1.3\) says:

\(\displaystyle D = b_02^0 + b_12^1 + b_22^2 + \cdots + b_{N-1}2^{N-1}\)

But since the question used the letter \(\displaystyle D\) for the digital word, I would change the letter of the equation to avoid confusion.

\(\displaystyle E = b_02^0 + b_12^1 + b_22^2 + \cdots + b_{N-1}2^{N-1}\)

where \(\displaystyle E = v_A\)

 

[khansaheb]

Eq. 1.3\displaystyle 1.31.3 says:

where is equation 1.3 first shown?

(see Eq. 1.3\displaystyle 1.31.3)

Where?.................