In this lab, the students will obtain experience with sequential lo...
Question
In this lab, the students will obtain experience with sequential logic design, and study digital design using the Xilinx design package for FPGAs. It is assumed that students are familiar with the operation of the Xilinx design package for Field Programmable Gate Arrays (FPGAs) through the Xilinix tutorial available in the class website.
1. This lab introduces unsigned binary division algorithms, including the restoringalgorithm.
2. Given a dividend ‘a’ and a divisor ‘b’, the restoring division algorithm calculates the quotient ‘q’ and the remainder ‘r’ such that a = b x q + r and r < b, by subtracting b from the partial remainder (initially the MSB of a). If the result of the subtraction is not negative, we set the quotient bit to 1. Otherwise, b is added back to the result to restore the partial remainder. Then we shift the partial remainder with the remaining bits of ‘a’ to the left by one bit for the calculation of the next quotient bit. This procedure is repeated until all the bits of ‘a’ are shifted out.
3. Figure 1 shows the schematic diagram of a restoring divider. There are three registers: reg_b, reg_r, and reg_q, for storing the divisor b, a remainder r, and quotient q respectively. Initially, reg_q stores the dividend a. A subtracter is used to subtract b from the partial remainder. The MSB of the output of the subtracter is used to determine whether the result of the subtraction is negative or not.
The multiplexer over reg_q is used to load a initially and to shift the content of reg_q (a and q) to the left later. The multiplexer over reg_r implements the restoring. If the result of the subtraction is negative, the multiplexer selects the original partial remainder. Otherwise, it selects the result of the subtraction. At each iteration, one bit of q is obtained from the sign bit of the subtracter result and written to the LSB of the reg_q.
4. In Figure 2, start signal means the start of the division; busy indicates that the divider is busy (can’t start a new division); ready indicates that the quotient and remainder are available; and count is the output of a counter that is used to control the iterations of the division.
5. Figure 2 shows part of the expected output of the simulation of 0x4c7f228a / 0x6a0e, q = 0xb8a6 and r = 0x4d76 are available when ready is 1 at 330 ns and then 0xffff00/4, q is 0x3fffc0, and r is 0.
6. Write a behavioral Verilog code describing Figure 1. Compile and simulate your code to correctly do the division.
7. Write a report that contains the following:
a. Your Verilog design code. Use:
i. Device: XC7Z010- -1CLG400C
b. Your Verilog Test Bench design code to do the following division shown in item 5 (0x4c7f228a / 0x6a0e). Add “`timescale 1ns/1ps” as the first line of your test bench file.
c. The waveforms resulting from the verification of your design with ModelSim showing all the signals as shown in Figure 2. Show the signals till 680 ns.
d. The design schematics from the Xilinx synthesis of your design. Do not use any area constraints.
e. Snapshot of the I/O Planning and
f. Snapshot of the floor planning
1. This lab introduces unsigned binary division algorithms, including the restoringalgorithm.
2. Given a dividend ‘a’ and a divisor ‘b’, the restoring division algorithm calculates the quotient ‘q’ and the remainder ‘r’ such that a = b x q + r and r < b, by subtracting b from the partial remainder (initially the MSB of a). If the result of the subtraction is not negative, we set the quotient bit to 1. Otherwise, b is added back to the result to restore the partial remainder. Then we shift the partial remainder with the remaining bits of ‘a’ to the left by one bit for the calculation of the next quotient bit. This procedure is repeated until all the bits of ‘a’ are shifted out.
3. Figure 1 shows the schematic diagram of a restoring divider. There are three registers: reg_b, reg_r, and reg_q, for storing the divisor b, a remainder r, and quotient q respectively. Initially, reg_q stores the dividend a. A subtracter is used to subtract b from the partial remainder. The MSB of the output of the subtracter is used to determine whether the result of the subtraction is negative or not.
The multiplexer over reg_q is used to load a initially and to shift the content of reg_q (a and q) to the left later. The multiplexer over reg_r implements the restoring. If the result of the subtraction is negative, the multiplexer selects the original partial remainder. Otherwise, it selects the result of the subtraction. At each iteration, one bit of q is obtained from the sign bit of the subtracter result and written to the LSB of the reg_q.
4. In Figure 2, start signal means the start of the division; busy indicates that the divider is busy (can’t start a new division); ready indicates that the quotient and remainder are available; and count is the output of a counter that is used to control the iterations of the division.
5. Figure 2 shows part of the expected output of the simulation of 0x4c7f228a / 0x6a0e, q = 0xb8a6 and r = 0x4d76 are available when ready is 1 at 330 ns and then 0xffff00/4, q is 0x3fffc0, and r is 0.
6. Write a behavioral Verilog code describing Figure 1. Compile and simulate your code to correctly do the division.
7. Write a report that contains the following:
a. Your Verilog design code. Use:
i. Device: XC7Z010- -1CLG400C
b. Your Verilog Test Bench design code to do the following division shown in item 5 (0x4c7f228a / 0x6a0e). Add “`timescale 1ns/1ps” as the first line of your test bench file.
c. The waveforms resulting from the verification of your design with ModelSim showing all the signals as shown in Figure 2. Show the signals till 680 ns.
d. The design schematics from the Xilinx synthesis of your design. Do not use any area constraints.
e. Snapshot of the I/O Planning and
f. Snapshot of the floor planning
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Top Level Diagram of Restoring Divider
Given a dividend ‘a’ and a divisor ‘b’, the restoring division algorithm calculates the quotient ‘q’ and the remainder ‘r’ such that a = b x q + r and r < b, by subtracting b from the partial remainder (initially the MSB of a). If the result of the subtraction is not negative, we set the quotient bit to 1. Otherwise, b is added back to the result to restore the partial remainder. Then we shift the partial remainder with the remaining bits of ‘a’ to the left by one bit for the calculation of the next quotient bit. This procedure is repeated until all the bits of ‘a’ are shifted out.
The Pinout description of the top level module is described in Figure 1.
Preferred Modelling Style
The code has been written using structural modelling style. Structural modeling / Hierarchical modeling has been kept in mind before designing the below Restoring Divider. Verilog provides the concept of a module. A module is the basic building block in Verilog. A module can be an element or a collection of lower-level design blocks.
The Restoring Divider depicted in the diagram below has different blocks to it.
Register ( REG_Q, REG_B & REG_R)
Subtractor
Mux (MUX_Q, MUX_R)
These blocks have been coded in Verilog separately and then are grouped into the top level module with required interconnections. A Control Unit and a Counter have been coded separately and they are also grouped into the top level module to ensure the fourth point mentioned in the lab.
Control Unit
This component is a Finite State Machine which controls the complete process. A finite state machine (FSM) is a kind of sequential circuit which is designed to sequence/step through specific/defined patterns of finite states in a predetermined sequential manner. It is capable of storing the status of something at a given time and operate on input to change the state as well as status of the dependent outputs. There are two types of FSM, Mealy and Moore. The Moore FSM has outputs that are a function of current state only. The Mealy FSM has outputs that are a function of the current state and primary inputs.
Given a dividend ‘a’ and a divisor ‘b’, the restoring division algorithm calculates the quotient ‘q’ and the remainder ‘r’ such that a = b x q + r and r < b, by subtracting b from the partial remainder (initially the MSB of a). If the result of the subtraction is not negative, we set the quotient bit to 1. Otherwise, b is added back to the result to restore the partial remainder. Then we shift the partial remainder with the remaining bits of ‘a’ to the left by one bit for the calculation of the next quotient bit. This procedure is repeated until all the bits of ‘a’ are shifted out.
The Pinout description of the top level module is described in Figure 1.
Preferred Modelling Style
The code has been written using structural modelling style. Structural modeling / Hierarchical modeling has been kept in mind before designing the below Restoring Divider. Verilog provides the concept of a module. A module is the basic building block in Verilog. A module can be an element or a collection of lower-level design blocks.
The Restoring Divider depicted in the diagram below has different blocks to it.
Register ( REG_Q, REG_B & REG_R)
Subtractor
Mux (MUX_Q, MUX_R)
These blocks have been coded in Verilog separately and then are grouped into the top level module with required interconnections. A Control Unit and a Counter have been coded separately and they are also grouped into the top level module to ensure the fourth point mentioned in the lab.
Control Unit
This component is a Finite State Machine which controls the complete process. A finite state machine (FSM) is a kind of sequential circuit which is designed to sequence/step through specific/defined patterns of finite states in a predetermined sequential manner. It is capable of storing the status of something at a given time and operate on input to change the state as well as status of the dependent outputs. There are two types of FSM, Mealy and Moore. The Moore FSM has outputs that are a function of current state only. The Mealy FSM has outputs that are a function of the current state and primary inputs.
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