**Q1. (A) Implement the following Boolean function using only NAND logic gates: $f(a,b,c)=a\cdot b'+b\cdot c$** The correct equation is *$f(a,b,c)=\textrm{NAND}(\textrm{NAND}(a,\textrm{NAND}(b,b)), \textrm{NAND}(b,c))$.* The circuit diagram is: ![[Midterm Question 1 Answer Circuit Diagram.png]] > [!note] From ChatGPT > The NAND gate equivalents for NOT, AND, and OR are: > $\overline x=\textrm{NAND}(x,x)=(x\cdot x)'$. > $x\cdot y=\textrm{NAND}(\textrm{NAND}(x,y),\textrm{NAND}(x,y))=((x\cdot y)'\cdot(x\cdot y)')'$. > $x+y=\textrm{NAND}(\overline x,\overline y)=((x\cdot x)'\cdot(y\cdot y)')'$. > > Starting from the most basic term, which in this case is $b'$, you convert them to NAND gates using these equivalencies. ^6f0ce0 **Q(2). Write the optimized Boolean function for $f(x_1,x_2,x_3,x_4)=\sum m(0,2,4,5,7,8,9,15)$** ... **Q(3). (A) Optimize the following Boolean function: $f(a,b,c)=b\cdot c+a'\cdot b\cdot c'+a'\cdot b'\cdot c'+b\cdot c'$** ... **(B) Generate and optimize Sum-of-Product (SOP) from the following truth table:** | $A$ | $B$ | $C$ | $F$ | | --- | --- | --- | --- | | 0 | 0 | 0 | 1 | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 1 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 1 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | | 1 | 1 | 1 | 1 | ...