(Solved): NOTE: Some questions require drawing schematics. You can use Logisim Evolution for drawing a sche ...

NOTE: Some questions require drawing schematics. You can use Logisim Evolution for drawing a schematic and then take a screenshot. Please see the Logisim Tutorial on Canvas as needed. Let \( A B C D_{2} \) be a 4-bit non-negative integer with corresponding decimal values: \[ \begin{array}{l} 0000_{2}=0_{10} \\ 0001_{2}=1_{10} \\ 0010_{2}=2_{10} \\ 0011_{2}=3_{10} \\ \ldots \\ 1111_{2}=15_{10} \end{array} \] The digits \( A, B, C \), and \( D \) in this 4-bit integer are also to be considered variables. Consider two functions of these 4 variables \( f(A, B, C, D) \) and \( g(A, B, C, D) \). 1. The function \( f(A, B, C, D) \) is defined as: \[ f=\left\{\begin{array}{lc} 1 & \text { if the hex value of } A B C D_{2} \text { is less than } A_{16} \\ 0 & \text { otherwise } \end{array}\right\} \] Describe \( f \) in the following forms listed below: (a) Truth Table (b) CSOP in the concise \( \sum m_{i} \) notation (c) CPOS in the concise \( \Pi \boldsymbol{M}_{i} \) notation 2. The function \( g(A, B, C, D) \) is defined as: \[ g=\left\{\begin{array}{ll} 0 & \text { if } f=1 \\ 1 & \text { if } f=0 \end{array}\right\} \] Describe \( g \) in the following forms listed below: (a) CSOP in the concise \( \Sigma m_{i} \) notation (b) CPOS in the concise \( \Pi \boldsymbol{M}_{\mathrm{i}} \) notation 3. Express the function \( f(A, B, C, D) \) in the following forms: (a) A Boolean Algebra expression of the CSOP function \( f(A, B, C, D) \) (b) A minimized Boolean expression for \( f(A, B, C, D) \) Use the properties and axioms of Boolean Algebra to minimize \( f(A, B, C, D) \)