# Arithmetic Circuits Lab (4-bit multiplier, 2-bit multiplier, 8-bit adder, and an 8-bit multiplexer)

# 1. DEFINITION OF THE PROBLEM

Make certain types of circuits with storage elements and analyze the complexity of the problem, using the tool called LOGISIM, which is a free software tool to design and simulate digital electronic circuits based on a graphical interface, this software comes with the license package is published by GNU, and can be run on different platforms.

In this laboratory we will test the functionality of the circuit designs proposed in laboratory guide 2, using the LOGISIM tool, to carry out the schematic or structural designs of the circuits and verify their operation.

# RESEARCH BACKGROUND

To carry out the circuits, you must have prior knowledge of the operation of the LOGISIM software, remember the principles of the use of this program that have been worked on in the chair, the previous reading of the class study material and the laboratory guide is also involved, some doubts about the structure of the circuits were resolved through internet searches.

# 2. HYPOTHESIS PROPOSAL

With the LOGISIM program, the designs of the circuits with storage elements will be carried out and the correct operation of these will be tested, with the help of the study material and the guide, the objectives will be met.

# 3. DEFINITION OF DEPENDENT VARIABLE

In this practice we will use LOGISIM, where we need the laboratory guide, and the collaboration of the teacher, we will define the results that we want to obtain and procedures to carry out. The laboratory procedure will be carried out according to the laboratory guide 2.

# 4. DEFINITION OF THE EXPERIMENTAL SUBJECT

**drawing the circuit**: The circuits will be made based on the design and the components proposed in the guide so that the device works correctly.

**Analyzing the circuit:** The operation of the circuit will be verified, providing the truth tables so that the gates have the exact numbers

# 1. IDENTIFICATION OF INDEPENDENT VARIABLES

**The development of**:

-Schematic design of the 'Latch D'

-Schematic design of the 'Flip-Flop D'

-Hierarchical design of a 'Flip-Flop T'

-Hierarchical design of a shift record

# 2. DEFINITION OF TREATMENT

## 2.1 MATERIALS AND SUPPLIES

LOGISIM

LABORATORY GUIDE 2

CLASS MATERIALS

## 2.2 PROCEDURE

The circuits with storage medium are carried out according to the guide, taking into account the principles of circuits with storage elements learned in class, taking evidence of their operation, and analyzing their structure and results to draw conclusions based on the information obtained. in the circuits made.

**Schematic design of the 'Latch D'**

Latch D is an asynchronous bistable circuit used to store information in digital systems, also known as transparent latch because the level present in D will be stored in the latch at the moment the input **enable** is activated, generally through a high state, that is to say 1. Having two inputs for data entry will have 4 possible combinations and these define the state of **Q **as shown in the truth table.

**Latch D truth table Latch D schematic design**

**Schematic design of the 'Flip-flop D'**

The D Flip-Flop is a bistable circuit, it is useful when you need to store a single bit of data in this circuit. **Q **follow **D. **at each clock pulse, for this the device has two states, and the output is the value of the input **D. **when the sync input is activated **C. **and depending on the activation mode of this synchronism input, there are two types, active in latch (by level) and active up or down (by flank), the characteristics of this circuit are used for signal processing

The truth table for Flip-Flop D is shown below.

** Flip-Flop D truth table Schematic design of the 'Flip-flop D'**

**Hierarchical Design of a 'T Flip-flop'**

**HERE PRRO EDIT FROM HERE FORWARD**

The 2-bit multiplier is the bare minimum circuit to make to build an arithmetic operation in a simulator or some other tool. The maximum result will be “9”, and the minimum result will be “0”. The entries will be A (A1 and A0) and B (B1 and B0). There are two ways to perform this multiplication. The first by means of a truth table, the inputs are the two numbers to be multiplied and the output is the result. The second way is to do normal multiplication and use half adders. In this laboratory we will carry out the exercise through multiplication.

** 2-bit multiplier truth table 2-bit multiplier logic gate circuit**

**8 bit multiplier**

The following circuit is a multiplier of 2 4-bit numbers. It has two inputs A (A3, A2, A1, A0) and B (B3, B2, B1, B0), which can take the values from 0 to 15. It will have a minimum result of 0 and a maximum of 225.

The method used for the design will be that of direct multiplication, that is, first all the multiplications between bits are performed using the and gates, and then the additions are performed using the adders. A 4-bit multiplication is as shown below.

# 1. CONCLUSIONS

In this laboratory it was possible to observe the operation of the circuits with storage elements and their interaction with the data satisfactorily, through modeling and simulation in the LOGISIM tool, and with this to see how these elements of the memory units of the computers work. common