Introduction about your project, describe the problem, and your solution. Project truth tables, expressions, k-maps and any related task must included here. Also project documentation must included.

In this project students should work in groups of 3 to implement a fully functioning sequential circuit. This sequential circuit should work as a Buffer, a competition circuit, or 4-way light circuit depending on the student's choice. The idea of the three projects will be explained in the lab. To design the circuit, Logisim should be used. Students should submit their software implementation and the report here.

• Moath Khalid Alahmadi
• Maan Almazroei
• farez Alghazzawi

• Moath 33% Subtraction
• Maan 34% Multiplication
• Farez 33% Addition

This circuit is used to perform three arthimatic operations Addition, Subtraction, and Multiplication of two numbers with 8 bits. Students required to build required components from the basic logic gates (AND, OR, XOR, NOT gates). Implementation should contains design of half adder, full adder, and 8 bits parallel binary adder. Subtraction and Multiplier should implemented using full adder as described in following diagrams. You are not allow to use pre-designed Adder, Subtractor, and Multiplier, you mush build them from scratch.

From above design you can expaned it to implement 8-bit parallel binary adder.

An enable input to activate subtractor output or deactivate.

The implementation of multiplier contains several components. One of them is an AND gate with $b_i$ with every bit in $A$.

You need to use above component several times to perform multiplication of 8-bits input with 8-bits input. Here an example of multipling 2-bits with 8-bits.

As you can see the outout is the total number of bits in the inputs (2 + 8). We mark the first 8 bits as ($lo$) bits and the remaining 2 bits as ($hi$).

Here another example of 8-bits input multiplied with 3-bits input:

So you need to repeate this pattern until to you complete the design of 8-bits for $B$.

The following design is combination of all the three arthimatic operation. As you can see in diagram there is 2x4 Decoder to choose operation:

0: Addition 1: Subtraction 2: Multiplication

Each selection will activate only one operation and disable the other two operation.

Learn how to build 8-bit calculator to perform three arithmetic operation addition, subtraction, and multiplication of two variables of 8-bit each using logic gates and plexers. Three circuit were designed to perform the three operation and finally connect them together as one circuit with decoder to select one operation at a time.

The function of the adder circuit is to add two variables ( A and B) 8 bits each. It integrated in the final combination with two other circuits (Addition and subtraction circuits) to work together as a calculator.

1. Half Adder
2. Full Adders (consists of two half adders)
3. OR gate

• Three inputs A and B (both has 8 bits) along with Carry in are applied to the Full Adder.

• The Full Adder output is SUM and Carry out.

• 8 Full Adders are connected together to generate summation of the two 8 bits inputs (A and B) plus carryout

The main function of this circuit is to perform subtraction of two variables of 8-bit each (A-B).

• 8-bit binary subtractor
• Controlled buffer

The circuit subtract two 8-bits binary numbers. There is two inputs "A" & "B". The value of "B" is subtracted from "A". The circuit output is controlled by a controlling buffer to enable or disable the circuit.

1. We perform 2nd compliment on (B). which means converting 1 to 0 and vice versa.
2. Add 1 to (B’) to become (b’’).
3. Now we add (A) with (B’’) and we will get the result of the subtraction.

• A: 1110010 (Decimal =114)
• B: 1000101 (Decimal = 69)
• Now perform step1 on B
• B’: 0111010
• Then perform step2 on B’
• B’’: 0111011
• Then perform step3 add A on B’’.
• A: 1110010
• B’’: 0111011
• ---------------- +
• 0101101 (This equivalent to 45 Decimal)

To subtract any other number those the steps to do it. In the final circuit they will be 4 input ‘A’ ‘B’ in the form of 8-bit input, ‘Cout’ input always 0 which in the circuit is ground. ‘Enable’ input is used to make the subtractor circuit on when the decoder choose number ‘2’. This makes sure there is no overlap between the other circuit.

The function of the multiplier circuit in this project is to perform multiplication of two binary numbers 8 bits each. And It integrated in the final combination with two other circuits (Addition and subtraction circuits) to work together as a calculator.

• Half adder
• Full adder
• 8-bit binary adder
• 8x8 Multiplier

• Two inputs A & B, the number which is to be multiplied by the other number is called multiplicand (A) and the number multiplied is called multiplier (B).
• Eight Logic circuits of input A and B, each consists of 8 AND gate.
• Seven 8-bit parallel binary Adders
• Two controlled buffer gates for enabling connecting to High and Low outputs

Multiplication in binary numbers is performed by similar method of multiplication of decimal number system. The multiplication process of 8x8 bits is performed as follow: 1st. step: multiply the whole 8 bits of multiplicand (A) by the first digit of the multiplier (B). 2nd. step: multiply the whole 8 bits of multiplicand (A) by the second digit of the multiplier (B). 3rd. step: shift the result of second step to the left by one digit. 4th. step : repeat steps 1, 2 and 3 until completing the whole 8 digits of multiplier (B). Finally: make summation for the above 8 multiplication results.

These steps are performed in the logic circuit by applying two inputs to AND gate representing Ai and Bi, the first digit of the product result in each step of multiplication process is connected directly to the final output port of the multiplication circuit (by-passing the Adder). By the end of the multiplication process, the total number will be 8 digits which are named Lo Output.

The initial carry in is considered to be zero. The the subsequent carry out of each step is connected to the next step. By the end of the multiplication process, the total number will be 8 lines which are named Hi Output.

In order to enable/disable the output of the multiplier, two controlled buffer gates are connected to the Lo and Hi outputs. The controlled buffer gate is three-state buffer, it works as a switch to switch ON or OFF the output based on the control signal (enable or disable).

The final circuit is a combination of the three individual circuit of addition, subtract, and multiplication. We used 2x4 decoder to enable the circuit that we want to operate and disable the other two circuit. When the input of the decoder is "00" the addition circuit will be enabled and perform addition for the two variables (A+B). When the input is "01" the subtraction circuit will operate and subtract "B" from "A". When the input is "10" the multiplication circuit will work and multiply A by B.

A multiplexers was added to the circuit before the Lo(output) just to make sure we are getting the result from the right circuit. Another multiplexer is used to fromat the Hi(output). Without using the last multiplexer, the circuit will run into some errors. Ground signal was made for the additional and subtraction circuits to work.

1. Calculator

Each student's grade will defer from his group-mate

• content and organization
• stating the problem need to be solved
• explanation of each component used
• explanation of whole circuit/integration of component
• how often you update/participate/contribute in group repository

Monday 29 / 7 / 1444 H, 20 Feb. 2023

Include exported image from Logisim of your project here. (Screenshot is not accepted!)