Draw a circuit which produces Sum and CarryOut from inputs A and B (this circuit is known as a half adder). You should use exactly one AND gate and one XOR (exclusive or) gate.

Design a code converter that converts an unsigned number a into its negative 2's complement representation -a. Specifically, the circuit has two inputs: a1 and ao, and three outputs: b1 and bo (the equivalent to -a) and valid, which is 1 when -a can be represented in 2's complement and O otherwise. 1. Write the truth table for the code converter. 2. Give the simplest SOP expressions for the functions b1, bo, and valid.

PROBLEM 2 4-bit decrement In class we considered an increment circuit that adds 1 to its input value. Now we want a circuit that subtracts 1 (i.e., z = x − 1). Draw a 4-bit decrement circuit that does not use not gates. -

Design a 16 bit adder/subtractor with 2 data inputs (B15 to B0 and A15 to A0), a SEL input (1 if add and 0 if subtract), and a result output (R15 to R0).You can design the circuit in MultiSim, VHDL, or LabVIEW. PLEAE USE MULTISIM

0 0 0 0 (a) Complete the following truth tables by simulating the 3-input circuits implemented in the previous steps. Input1 Input2 Input3 0 0 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 Output of 3-input built-in XOR gate Output of 3-input XOR gate in Step4(c)

Draw a circuit that uses only one AND gate and one OR gate to realize each of the following functions: (a) ABCF + ACEF + ACDF

Write a Boolean expression for a NOR gate. F(A, B) = Write the Boolean expression for a four-input NOR gate. F(A, B, C, D) = To implement a 1-bit adder, write a Boolean expression for the Carry function. CarryOut(A, B, C;) = Input: A, B Carry in: C 2 pts 2 pts 2 pts

Give the symbol and truth table for the following gates: AND, OR, XOR, NAND and NOR. Do not forget to include the inputs and outputs wires.

4. A combinational circuit is defined by the following two Boolean functions: F₁ = B'C + AB F₂ = BC + AB Design the circuit with a decoder and two external OR gates.

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