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2. Simplify the output expressions. 3. Implement these circuits using AND, OR and XOR gates. 4. Cascade a half adder into a full adder and show how you can add two 2-bit numbers. Demonstrate this circuit to your lab instructor. 5. Question: What happens to the propagation delay of the N-bit full adder as N is increased from 2 bits to 32 bits? Compare and contrast this method of building an adder with the carry look ahead method described in your text book. What are the benefits and drawbacks of each? Part 2: 3-bit by 2-bit Multiplier Introduction Mathematics is one of the most common tasks a computer or other digital circuit is required to perform. Multiplication is a basic tool for mathematics, and is simply a series of additions of products, which is simple for humans at least. In a digital circuit, we are working with binary values, and therefore ANDs can be used to handle the product portion of the circuit. The multiplication algorithm for this lab follows the algorithm taught to people during primary education. Figure 1 is a graphical representation of the algorithm for multiplying a 3-bit binary number, B, by a 2-bit binary number, A. Solution bit 4 Solution bit 3 Solution bit 2 Solution bit 1 Solution bit 0 B2 B1 BO X A1 40 + $C_{out3}$ A1 \cdot B2 $A0 \cdot B2$ $A1 \cdot B1$ $A0 \cdot B1$ $A0 \cdot B0$ $A1 \cdot B0$ $A0 \cdot B0$ A1 \cdot B2 + $C_{out2}$ $A0 \cdot B2 + A1 \cdot B1 + C_{out2}$ $A0 \cdot B1 + A1 \cdot B0$ Procedure Figure 1. Graphical representation of multiplication algorithm. Using the full and half adder designs from part 1 of this lab, and the equations outlined in Figure 1, design and build a 3 bit x 2 bit multiplier. Demonstrate your working circuit to the lab instructor.

2. Simplify the output expressions.
3. Implement these circuits using AND, OR and XOR gates.
4. Cascade a half adder into a full adder and show how you can add two 2-bit numbers.
Demonstrate this circuit to your lab instructor.
5. Question: What happens to the propagation delay of the N-bit full adder as N is increased
from 2 bits to 32 bits? Compare and contrast this method of building an adder with the
carry look ahead method described in your text book. What are the benefits and
drawbacks of each?
Part 2: 3-bit by 2-bit Multiplier
Introduction
Mathematics is one of the most common tasks a computer or other digital circuit is required to
perform. Multiplication is a basic tool for mathematics, and is simply a series of additions of
products, which is simple for humans at least. In a digital circuit, we are working with binary
values, and therefore ANDs can be used to handle the product portion of the circuit. The
multiplication algorithm for this lab follows the algorithm taught to people during primary
education. Figure 1 is a graphical representation of the algorithm for multiplying a 3-bit binary
number, B, by a 2-bit binary number, A.
Solution bit 4
Solution bit 3
Solution bit 2
Solution bit 1
Solution bit 0
B2
B1
BO
X
A1
40
+
$C_{out3}$ A1 \cdot B2
$A0 \cdot B2$
$A1 \cdot B1$
$A0 \cdot B1$
$A0 \cdot B0$
$A1 \cdot B0$
$A0 \cdot B0$
A1 \cdot B2 + $C_{out2}$
$A0 \cdot B2 + A1 \cdot B1 + C_{out2}$
$A0 \cdot B1 + A1 \cdot B0$
Procedure
Figure 1. Graphical representation of multiplication algorithm.
Using the full and half adder designs from part 1 of this lab, and the equations outlined in Figure
1, design and build a 3 bit x 2 bit multiplier. Demonstrate your working circuit to the lab
instructor.

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