Design a combinational circuit that accepts a 4-bit number and generates a 3-bit binary number output that approximates the square root of the number. Round off the result. For example, if the square root of 2 is 1.4, give a result of 1 = 001. If the square root of 3 is 1.7, give a result of 2 = 010. Let ABCD as inputs and xyz as outputs.

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Can someone please help me with the multiplication part? How can I create the multiplier circuit using logic gate?

4 bit 2's Complement Multiplier INPUT A: 4 bit 2's Complement number INPUT B: 4 bit 2's Complement number OUTPUT: the product of A x B represented as a 8 bit 2's Complement number You are only allowed to use the basic gates: NOT, AND, OR, XOR. You may however, use these basic gates to build your own custom circuits (i.e. Adder). You are NOT ALLOWED to use Logisim's built in circuits. Each custom circuit is to be implemented as a sub-circuit as discussed in class. PART 2: Build a 8 bit controlled 2's Complement Inverter as a subcircuit named 8BitInverter

You are asked to design a circuit to detect if an overflow occurs when subtracting two integers represented in two's complement: Z= X - Y. Let Sz, Sx, and Sy be the sign bit for Z, X, and Y respectively, and they are fed as input to the circuit. Let O be the output bit of the circuit, whose value is 1 if an overflow happens, and 0 if otherwise. a) Build the truth table for O as a Boolean function of Sx, Sy, and Sz. b) Write the canonical expression (sum-of-product) for the Boolean function defined in the part a. c) Implement the Boolean expression defined in part b with a circuit by using AND, OR, and NOT gates. Draw the wiring diagram.

Q2. Two integer numbers A and B are represented in pure binary by two bits, being A=a₁a0 and B=b₁bo. e) A logic circuit provides the 4 bits output C=C3C2C1C0, as shown in the truth table below. FO a₁ 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 ao og 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 b₁ 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 Draw the logic circuits for c2. bo 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 C3 0 0 0 C2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 C1 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 Co 1 1 1 1 0 OO 0 0 0 1 1 1 1 0 ooo 0 0 0

Q2. Two integer numbers A and B are represented in pure binary by two bits, being A=a₁a0 and B=b₁bo. f) A logic circuit provides the 4 bits output C=C3C2C1C0, as shown in the truth table below. FO a₁ 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 ao og 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 b₁ 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 bo 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 C3 0 0 0 Draw an XOR gate and its truth table. C2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 1 1 C1 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 Co 1 1 1 1 0 OO 0 0 0 1 1 1 1 0 ooo 0 0 0

4 bit 2’s Complement Multiplier INPUT A: 4 bit 2’s Complement numberINPUT B: 4 bit 2’s Complement numberOUTPUT: the product of A x B represented as a 8 bit 2’s Complement number   Do this:Build a 4 Bit UNSIGNED Multiplier as a subcircuit named UnsignedMultiplier use AND gate ,full and half adders for the circuit

2. A 4-bit comparator has inputs A = 1101 and B = 1011. Complete the table below. gti Iti eqi Digit 3 gto Ito eqo gti Iti eqi Digit 2 gto Ito eqo gti Iti eqi Digit 1 gto Ito eqo gti eqi Digit 0 gto Ito eqo

Draw a circuit using 555 acts as a monostable.