Description

Indian Institute of Technology (IIT-Kharagpur)
COMPUTER SCIENCE AND ENGINEERING
Computer Organization and Architecture Laboratory
Lab–1
INSTRUCTIONS: Make one submission per group in the form of a single zipped folder containing your Verilog source code files(s) and Verilog testbench(es) only, and not the auxiliary files that ISE generates. Name your submitted zipped folder as Assgn 1 Grp <Group no>.zip and (e.g. Assgn 1 Grp 25.zip). Inside each submitted source and testbench files, there should be a clear header describing the assignment no., problem no., semester, group no., and names of group members. Liberally comment your code to improve its comprehensibility.
Introduction to Verilog Programming
In this assignment, we shall be designing and comparing two adder circuits using the Verilog Programming Language. The design shall be eventually prototyped on an FPGA and tested for its functionality on the hardware.
The first part of the assignment is on the design of the Ripple Carry Adder (RCA) and Carry Look-ahead Adder (CLA), which is a faster adder.
1. The first problem is on the design of a RCA. Write the Verilog Code for an n-bit adder. Proceed step by step as follows:
(a) A Half Adder is a combinational circuit, which takes in two input bits, a and b, and produces the sum bit, s and the carry-out bit, c. Write the truth-table for the assignments of s and c. Write the verilog code for the Half Adder.
(b) A Full Adder is a combinational circuit, which takes in three input bits, a, b, and in addition a carry-in bit c0, and produces the sum bit, s and the carry-out bit, c. Write the truth-table for the assignments of s and c in the Full-Adder. Write the verilog code for the Full Adder.
(c) Cascade 8 Full adders and create an 8-bit adder. These type of adders are called Ripple Carry Adders. Like-wise create, 16, 32, and 64 bit adders, and observe the longest delays in the circuits.
(d) How can you use the above circuit, to compute the difference between two n-bit numbers?
2. In the previous assignment, we have designed a Ripple Carry Adder (RCA). One of the weaknesses in the adder is the large delay because of the rippling of the carry, through what we call as the carry-chain. In this assignment, we endeavour to design a high-speed adder using the technique of what we call as the Carry Look-ahead Adder (CLA). In this exercise, we start with designing a 4-bit CLA and then use it to design a 16-bit CLA using a hierarchical structure.
Proceed as follows:
(a) First, design a 4-bit CLA. Clearly state, the Boolean equations of the Look-ahead carry generation for the 4 carry bits, C1, C2, C3, and C4 in terms of the generate and propagate signals, denoted as G0,…,G3 and P0…,P3 respectively. Also state the equations for the corresponding generate and propagate signals.
Computer Organization and Architecture Laboratory– 2 –
(b) Design the 4-bit CLA using verilog and compare its speed with a 4-bit RCA (ensure that the KEEP HIERARCHY option in your synthesizer is set TRUE). Check the correctness of the code by a test-bench in verilog and compare the speeds from the synthesis reports generated by the Xilinx tool.
(c) Now let us try to make a 16-bit adder in a hierarchical fashion. For this, we observe that C4 = G3 + P3G2 + P3P2G1 + P3P2P1G0 + P3P2P1P0C0. One can create the 16-bit adder in two ways. In both the ways, we reuse the 4-bit CLA just designed by you. However, in one of the ways we ripple in the carry out from the 4-bit CLA to the second stage, while in the other we compute the carry in of the second 4-bit CLA by using a separate level of Lookahead Carry Unit. This lookahead carry unit works on block propagates and block generates, denoted as P, G in the circuit shown in Fig 1. The definitions of the block propagate and block generate are as follows:
P = P3P2P1P0 (1) G = G3 + P3G2 + P3P2G1 + P3P2P1G0 (2)
Thus, we can write C4 = G + PC0. Now if you consider wrt. the Lookahead Carry Unit, this is the logic for the carry bit C1. Likewise, one can compute the logic for the carry bits, C2, C3, and C4 using the block propagates and generates. We also compute P3-0 and G3-0 which are block propagates and generates for the next level of the hierarchy (if one wishes to design 32 or 64 bit adders using this structure as a component). Note that the labels for the propagates and generates can be confusing, but since the labels are written internal to the blocks (or verilog modules) they dont conflict with each other. In this part you are supposed to:
(i) Augment the 4-bit adder to compute the block propagate and generate signals. Test the circuit using a testbench in verilog.
(ii) Design the Lookahead Carry Unit and integrate as shown in Fig 1.
(iii) Compare this circuit by annotating the delays for obtaining the sum and final carry out bits for the 16-bit adder, with that if the carry was rippled in (without using the second layer of lookahead).
(iv) Synthesize the results, and see how the speed and the LUT (lookup-table cost of the FPGA) compares with a 16-bit RCA.

Figure 1: The Hierarchical Structure of a 16-bit CLA