Check all correct representations of the following function. F(x.y,z) = x'y'z + xy'z' + xy'z + xyz' O (x+y+z)(x+y'+z)(x+y'+z')(x'+y'+z') (x+y'+z)(x+y'+z')(x+y'+z)(x+y+z') Ο Σ1.456) Ono,2,3,7) On(1,4,5,6) Σ(Ο237)
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- Write a function that makes the base conversion. It takes two integers n and b as input (n >= 0 andb > 1, both in base 10) and expresses n in base b. For example, the decimal expansion of 345 inbase 10 is 345 = 3 × 102 + 4 × 101 + 5 × 100.Sample input: n = 12, b =2. Sample output: 1100Explanation: (12)10 = (1100)2Keep the Diagram neat. Thanks. Implement the following boolean function using a) 16:1 mux b) 8:1 mux c) 4:1 mux F(A,B,C,D) =∑(0,1,2,7,8,10,11,13, 15)Write the equivalent infix expression for the following postfix expressions.a. x y * z + t -b. x y z + * w u / - c. x y - z u / * t s + -d. x y z w + - *
- Simplify or reduce the Boolean function below into three literals: F(P,Q,R) = (P + Q’R’)(PQ+R)+PQR’+P’RGiven the following definitions: U={a,b,c, d, e, f, g} A={a, c, e, g} B={a,b,c,d} find A n BNumbers can be regarded as product of its factors. For example,8 = 2 x 2 x 2; = 2 x 4.Write a function that takes an integer nand return all possible combinations of its factors.Note:You may assume that n is always positive.Factors should be greater than 1 and less than n.Examples:input: 1output:[]input: 37output:[]input: 12output:[ [2, 6], [2, 2, 3], [3, 4]]input: 32output:[ [2, 16], [2, 2, 8], [2, 2, 2, 4], [2, 2, 2, 2, 2], [2, 4, 4], [4, 8]].
- 2) Simplify the following Boolean expressions, using three-variable K-maps:F(x,y,z) = x′y′ + yz + x′yz′ PS:Please type instead of paper writingWrite pseudo code for a function to draw a regular N-gon. Arguments for the function are location (x,y) and radius r.(Practice) State whether the following are valid function names and if so, whether they’re mnemonic names that convey some idea of the function’s purpose. If they are invalid names, state why. powerdensity m1234 newamp 1234 abcd total tangent absval computed b34a 34ab volts$ a2B3 while minVal sine $sine cosine speed netdistance sum return stack
- Consider the following function someFunc::Integer -> Integer -> Integer -> Integer someFunc x y z = x *(y + z) Prove that someFunc a b c = sumFunc a c bGiven a boolean expression consisting of the symbols 0 (false), 1 (true), & (AND), I (OR), and /\ (XOR), and a desired boolean result value result, implement a function to count the number of ways of parenthesizing the expression such that it evaluates to result. The expression should be fully parenthesized (e.g., ( 0) A( 1)) but not extraneously (e.g., ( ( ( 0)) /\ ( 1)) ). EXAMPLE countEval("l/\01011", false) -> 2 countEval("0&0&0&1All0", true)-> 10For function F(a,b,c) = ∑[sum symbol] m(1,3,4,6), which one is equal to F in POS form? A ) F(a,b,c) =(a'.b'.c') + (a'.b.c')+ ( ab'c )+( abc ) B ) F(a,b,c) =(a'+b'+c').(a'+b+c') (a+b'+c')(a+b+c) C ) F(a,b,c) =(a+b+c).(a+b'+c) (a'+b+c')(a'+b'+c') D ) F(a,b,c) =(a.b.c) + (a.b.c)+ (a'bc')+(a'b'c')