3. Use a Don't care Karnaugh map to nd a minimal representation for a Boolean expression H1335 z] agreeing with the inputla'output table below. one 1 001 1113:!!in 0111 u 011 z 1013 - 101 1 2 11a 1 111 u 4. [a] (i) What is the smallest positive number that can be written in normalised scientic notation with mantissa of 5 digits and exponent between 25U and 2510' inclusive? {ii} What is the biggest positive number that can be written in normalised scientific notation with mantissa of 5 digits and exponent between 25 and 25D inclusive? (b) Carry out the following calculations and express the answer in normalized scientic notation with a 4 digit mantissa and exponent between 25i] and 25D inclusive. (i) ((121121 x 11122\") x [0.3129 x 10-111} {ii} ((121121 x 1022\"} + [D3129 x 10-111} {iii} [new x 1022\"} + [0.1931 x 1021?} (iv) (11.21121 x 11121\") {11.1931 x 111217} 5. Let x} 2 214 + 3x3 + 5'12 + 6. [a] Write the polynomial x} in the telescoping Form, showing each step of the factorisation. (b) Evaluate the polynomial x} when x = B by completing the Following memory table For Horner's algorithm (add more rows if needed]. Hint: rst identify Np: and the coefcients A[D},A{1],...,A[N}. 1.51A[N) 2. ForK=1toNa. Srx:S+A{NK) 1 (c) With no calculation, convert 2371363 to base If], and explain why your answer is correct