Q3. Given f(a, b, c, d) = acd + b'd + a'cd + ab'cd + a'b'cd'. (a) Express f as a minterm expansion (use m-notation). (b) Express f as maxterm expansion (use M-notation). (c) Express f ' as a minterm expansion (use m-notation). (d) Express f ' as a maxterm expansion (use M-notation). Q4. A switching circuit has two control inputs (C1 and C2), two data inputs (X1 and X2), and one output (Z).The circuit performs logic operations on the two data inputs, as shown in this table: C1 C2 | FUNCTION 0 0 | X1 . X2 0 1 | X1 + X2 1 0 | X1?X2 1 1 | X1?X2 (a) Derive a truth table for Z. (b) Use a Karnaugh map to find a minimum OR-AND gate (POS) circuit to realize Z.
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5. A switching circuit has 2 control inputs C1 and C2, two data inputs X1 and X2, and one output Z. The circuit performs one of the logic operations: NAND, NOR, XOR and EQU (Equivalence) on the two data inputs. The function performed depends on the control inputs: C1 C2 Function 0 0 XNOR 0 1 NAND 1 0 NOR 1 1 XOR (a) Derive a truth table for Z (b) Use Karnaugh map to find a minimum AND-OR gate circuit to realize Z.
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A combinational circuit has 3 inputs A, B, C and output F. F is true for the following input combinations: A is False, B is True, C is True; A is False, B is False, C is True; A is False, B is True, C is False; A is False, B is False, C is False. i. Write the table for F. Use the convention True=1 and False=0. (2) ii. Write the simplified expression for F in SOP form. (1) iii. Write the simplified expression for F in POS form. (1) iv. Draw a logic circuit using the minimum number of 2-input NAND gates. (2)
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