This document describes the implementation of an 8-bit Booth multiplier using Verilog code. It includes an introduction to Booth's multiplication algorithm, which multiplies two signed binary numbers in two's complement notation. The architecture of the 8-bit Booth multiplier is shown in a block diagram. Verilog code for the Booth multiplier is provided, along with a testbench. Schematic and symbol diagrams illustrate the design. Simulation waveforms confirm the multiplier works as intended. In conclusion, Booth multipliers are found to have advantages over combinational multipliers in terms of area and complexity.

1. PROJECT ON DIGITAL VLSI DESIGN
8-BIT BOOTH MULTIPLIER
SUB CODE: ECE419
SUBMITTED BY
DINESH DEVIREDDY
Regid-11502811(01)
Section-E1513
SUBMITTED TO
AMANDEEP SINGH
(ASSISTANT PROFESSOR)

2. INTRODUCTION: Booth's multiplication algorithm is a
multiplication algorithm that multiplies two signed binary numbers in
two's complement notation. The algorithm was invented by Andrew
Donald Booth in 1950 while doing research on crystallography at
Birkbeck College in Bloomsbury, London. Booth used desk calculators
that were faster at shifting than adding and created the algorithm to
increase their speed. Booth's algorithm is of interest in the study of
computer architecture.
HOW BOOTH MULTIPLIER WORK: Booth's algorithm
examines adjacent pairs of bits of the N-bit multiplier Y in signed
two's complement representation, including an implicit bit below the
least significant bit, y−1 = 0. For each bit yi, for i running from 0 to N
− 1, the bits yi and yi−1 are considered. Where these two bits are
equal, the product accumulator P is left unchanged. Where yi = 0 and
yi−1 = 1, the multiplicand times 2i is added to P; and where yi = 1 and
yi−1 = 0, the multiplicand times 2i is subtracted from P. The final
value of P is the signed product. The representations of the
multiplicand and product are not specified; typically, these are both
also in two's complement representation, like the multiplier, but any
number system that supports addition and subtraction will work as
well. As stated here, the order of the steps is not determined.
Typically, it proceeds from LSB to MSB, starting at i = 0; the
multiplication by 2i is then typically replaced by incremental shifting
of the P accumulator to the right between steps; low bits can be
shifted out, and subsequent additions and subtractions can then be
done just on the highest N bits of P.[1] There are many variations and
optimizations on these details. The algorithm is often described as
converting strings of 1s in the multiplier to a high-order +1 and a low-
order −1 at the ends of the string.

3. 8x8 Signed Booth Multiplier:
In the given booth multiplier we use Verilog code to produce the
output and images below summarize the design and implementation
of the signed Booth multiplier.
ARCHITECTURE :
The above block diagram explains the design and implementation of
the signed Booth multiplier

4. 8-bit Verilog Code for Booth’s Multiplier
module multiplier(prod, busy, mc, mp, clk, start);
output [15:0] prod;
output busy;
input [7:0] mc, mp;
input clk, start;
reg [7:0] A, Q, M;
reg Q_1;
reg [3:0] count;
wire [7:0] sum, difference;
always @(posedge clk)
begin
if (start) begin
A <= 8'b0;
M <= mc;
Q <= mp;
Q_1 <= 1'b0;
count <= 4'b0;
end
else begin
case ({Q[0], Q_1})
2'b0_1 : {A, Q, Q_1} <= {sum[7], sum, Q};
2'b1_0 : {A, Q, Q_1} <= {difference[7], difference, Q};

5. default: {A, Q, Q_1} <= {A[7], A, Q};
endcase
count <= count + 1'b1;
end
end
alu adder (sum, A, M, 1'b0);
alu subtracter (difference, A, ~M, 1'b1);
assign prod = {A, Q};
assign busy = (count < 8);
endmodule

6. TESTBENCH:
module testbench;
reg clk, start;
reg [7:0] a, b;
wire [15:0] ab;
wire busy;
multiplier multiplier1(ab, busy, a, b, clk, start);
initial begin
clk = 0;
$display("first example: a = 3 b = 17");
a = 3; b = 17; start = 1; #50 start = 0;
#80 $display("first example done");
$display("second example: a = 7 b = 7");
a = 7; b = 7; start = 1; #50 start = 0;
#80 $display("second example done");
$finish;
end
always #5 clk = !clk;
always @(posedge clk) $strobe("ab: %d busy: %d at time=%t", ab, busy,
$stime);
endmodule

7. SCHEMATIC DIAGRAM:
The above Schematic diagram explains the design and
implementation of the signed Booth multiplier

8. The above Symbol diagram explains the design and
implementation of the signed Booth multiplier
SIMULATION WAVE FORM:

9. CONCLUSION: It can be concluded that Booth Multiplier is
superior in respect like area, Complexity. In booth multiplier number
of gates is reduced and hence area of booth multiplier is less than
combinational multiplier. However Combinational Multiplier gives
optimum number of components required. Hence for less delay
requirement Booth’s multiplier is suggested. Further work can be
carried out on this project in the power estimation section and to
improve the speed or to minimize the delay and power of
multipliers.
REFERENCES:
:https://en.wikipedia.org/wiki/Booth's_multiplication_algorithm
:https://www.eecs.tufts.edu/~rjdang/Booth_Multiplier/EE103_Lab3_
Part1and3.pdf
THANKYOU