UPC EETAC Bachelor's Degree in Telecommunications Systems and in Network Engineering EEL

Chapter 1 problems

     - D1.11 -

10-bit arithmetic circuit for radix-2 and integer numbers

Products

D1.10

D1.12

1. Specifications

Design using plan C2 the 10-bit selectable adder subtractor comparator named Sel _add_subt_comp_10bit represented in Fig. 1a, a simplified arithmetic unit, targeting the given FPGA chip.

The same project B3.11 is proposed in Chapter 3 for learning the basics of μC software organisation and basic digital I/O.

Symbol

Fig. 1a. Arithmetic circuit for 10-bit radix-2 and integer numbers.

The circuit truth table signals are ordered as shown in Fig. 1b. Generate half of the table for N = '0' (data type radix-2) and the other half with N = '1' (data type integers). An example of table representation is in the highlighted P4.

 

Fig. 1b. Input and output order in the truth table. 

What is the range of operands and results?

You can consider several options for the test vectors, such:

 option #1: Radix-2 numbers for N = '0': 987, 345, 23, 1, 0, 14, 1023. Integer numbers for N = '1': (+33), (-33), (+510), (-510), (+92), (-39), 0

 option #2: Radix-2 numbers for N = '0': 333, 999, 45, 6, 0, 414, 1023. Integer numbers for N = '1': (+111), (-222), (+333), (-512), (+511),( -39), 0

 option #3: Radix-2 numbers for N = '0': 88, 777, 556, 12, 0, 433, 1023. Integer numbers for N = '1': (+99), (-99), (+444), (-444), (-511), (-18), 0

Draw the truth table. How long is it?

Draw an example of timing diagram to be used later as stimulus in the VHDL testbench when verifying the synthesised circuit. Suppose that Min_Pulse = 2.21 μs. How long does it take to simultate all the table combinations?

CPLD or FPGA target chip options:

 option #1: MAX II

 option #2: Cyclone IV

 option #3: MAX 10

 

2. Planning

Many arithmetic components are available in P4 and P3. And so, the idea is to apply our Plan C2 to draw a hierarchical top schematic based on components and signals.

The top entity may be conceived separating comparisons and additions/subtractions as shown in Fig. 2.

Top entity

Fig. 2. Project top entity architecture.

In this way, we can tackle the project divided in two main components. The idea of coparing natural numbers and integers in the same block, can be layed out in Fig. 3.

Selectable data comparisons

Fig. 3. The idea of data type selection for comparison operations.

The conceptual idea in Fig. 3 can be optimised because comparing integer numbers using a radix-2 comparators is not that difficult: see the algorith in this example Int_comp_8bit.

Optimised selectable comparator

Fig. 4. Optimised circuit for comparing integer and natural numbers.

The idea on how to implement an adder/subtractor for integer numbers is explained in this highlighted project: Int_add_subt_8bit. Only expanding the circuit size to 10-bit is required.

And thus, we can infer how to organise a module valid for both data types in Fig. 5.

IDea of a selectable adder-subtractor

Fig. 5. The conceptual idea of designing a circuit valid for two data types.

And, in the same way we did for the comparator, we can optimise the architecture of the sel_add_subt_10bit as represented in Fig. 6. Some control gates allow disabling the flag signals of no interest.

 

Selectable adder and subtractor for 10-bit operations

Fig. 6. Optimised adder-subtractor to reduce the component count.

Combining Fig. 6 as Chip2 and Fig. 4 as Chip1 we complete the top entity for this project in Fig. 2.

Let us consider these options:

option #1: Comp_4bit ---> plan A equations architecture; Comp_10bit ---> plan C2 reducing the 24-bit tree architecture shown in 74F85 datasheet to only 10-bit; Adder_4bit ---> plan C2 carry lookahead (CLA)

Project location:

 C:\CSD\P3\Sel_Add_Subt_Comp_10bit\Opt1\(files)

option #2: Comp_10bit ---> plan C2 ripple architecture using Comp_1bit based on the MoM; Adder_10bit --->  plan C2 ripple carry (RC) using Adder_1bit.

Project location:

 C:\CSD\P3\Sel_Add_Subt_Comp_10bit\Opt2\(files)

 

3. Development

Circuit synthesis

 

4. Test (functional)

Functional simulation

 

After having studied P4 lectures and LAB4 tutorials, the project can continue adding the fifth section on time measurements.

5. Test (gate-level)

 Additional questions can be added to our report. For instance: