3. Use a don't care Karnaugh map to find a minimal representation for a Boolean expression h(I, y, z) agreeing with the input /output table below. y z h(x, y, z) 0 0 X cy Z 1 X 0 2 X 4. (a) (i) What is the smallest positive number that can be written in normalised scientific notation with mantissa of 4 digits and exponent between -500 and 500 inclusive? (ii) What is the biggest positive number that can be written in normalised scientific notation with mantissa of 4 digits and exponent between -500 and 500 inclusive? (b) Carry out the following calculations and express the answer in normalized scientific notation with a 4 digit mantissa and exponent between -500 and 500 inclusive. (i) (0.2509 x 10250) x (0.7907 x 10-265 ) (ii) (0.2509 x 10250 ) x (0.7907 x 1045) (iii) (0.2509 x 10255) : (0.7907 x 10-265 ) (iv) (0.7907 x 10122 ) - (0.2509 x 10121) 5. (a) Calculate ged (350, 126) using the Greatest Common Divisor Algorithm (subtraction method ) by completing the memory table below (see question 1 of Practice Class 4B). gcd A gcd B Write Calculation 350 126 (b) Complete the following : ged (350, 126) = F . ..... 6. Let p(x) = 3x4 + 7x2 + 4x + 1. (a) Write the polynomial p() in the telescoping form, showing each step of the factorisation . (b) Evaluate the polynomial p(x) when a = 8 by completing the following memory table for Horner's algorithm (add more rows if needed). Hint: first identify N, a and the coefficients A(0), A(1), ..., A( N). Instruction K N-K A(N-K) S 1. S + A(N) 2. For K = 1 to N a. S + a*S + A(N-K) 1 (c) With no calculation, convert 30741, to base 10, and explain why your answer is correct