Question

For the binary input \(010\), which of the following represents min-term and max-term?

• A. \(x'yz',\ x+y+z\)
• B. \(x'yz,\ x+y'+z'\)
• C. \(xyz,\ x+y+z'\)
• D. \(x'yz',\ x+y'+z\)

Hint:

For min-term, \(0\) gives complemented variable. For max-term, \(1\) gives complemented variable.

Answer 1

The Correct Option is D

Concept:
For min-term, a variable is complemented when its value is \(0\), and uncomplemented when its value is \(1\). For max-term, a variable is uncomplemented when its value is \(0\), and complemented when its value is \(1\).

Step 1: Write the binary input. \[ 010 \] Assume variables are: \[ x,\ y,\ z \] So, \[ x=0,\quad y=1,\quad z=0 \]

Step 2: Find the min-term.
For min-term: \[ 0 \Rightarrow \text{complemented variable} \] \[ 1 \Rightarrow \text{uncomplemented variable} \] Thus, \[ x=0 \Rightarrow x' \] \[ y=1 \Rightarrow y \] \[ z=0 \Rightarrow z' \] Therefore, the min-term is: \[ x'yz' \]

Step 3: Find the max-term.
For max-term: \[ 0 \Rightarrow \text{uncomplemented variable} \] \[ 1 \Rightarrow \text{complemented variable} \] Thus, \[ x=0 \Rightarrow x \] \[ y=1 \Rightarrow y' \] \[ z=0 \Rightarrow z \] Therefore, the max-term is: \[ x+y'+z \] \[ \therefore \text{Correct Answer is (D)} \]