booth乘法节省面积、速度较移位相加速度也更快。
一个例子：14乘以-5，乘数和被乘数都用5bit补码表示，结果有10bit表示。
14的补码:01110, -5的补码11011 ，正确结果为-70：11 1011 1010
使用一个状态机实现这个乘法，IDLE下初始化等待数据输入，再进行加法和移位，次数由输入位宽决定，最后数据输出。
程序代码如下：
1: // **************************************************************
2:
3:
4: // File name : booth.v
5: // Module name : BOOTH
6: // Full name : multiply based on booth's algorithm
7: //
8: // Author : Yang Li
9: // Email : yangli0534@gmail.com
10: // Date : 2013/11/24
11: // Version : V 1.0
12: //
13: //Abstract : an implementation of multiplier based on booth's algorithm
14: // multiplier ,multiplicand :2's complement
15: //
16: // Modification history
17: // ------------------------------------------------------------------------------------------------------
18:
19: // *********************************************************************
20:
21: module booth
22: #(parameter WIDTH =8 )
23: (
24:
25: input wire sys_clk,
26: input wire sys_rst_n,
27: input wire [WIDTH-1:0] multiplicand,
28: input wire [WIDTH-1:0] multiplier,
29: input wire data_av,
30: output reg rfd,
31: output reg rdy,
32: output reg [2*WIDTH-1:0] product,
33: output reg [2*WIDTH-1:0] product_r
34: );
35: //*********************
36: //parameter DECLARATION
37: //*********************
38: localparam [3:0] IDLE = 4'b0001,
39: ADD = 4'b0010,
40: // TAP = 5'b00100,
41: SHIFT = 4'b0100,
42: DONE = 4'b1000;
43:
44: //localparam N= log2(WIDTH) ;
45: localparam N=5;
46: localparam WIDTH_PROD = 2*WIDTH;
47: //*********************
48: //INNER SIGNAL DECLARATION
49: //*********************
50: reg [WIDTH-1:0] multiplicand_add, multiplicand_minus;//鍔犺涔樻暟锛屽噺琚箻鏁
51: reg [WIDTH-1:0] upper_r, lower_r;//楂樺崐鍜屼綆鍗
52: reg booth_r; //booth bit
53: reg [3:0] state_curr, state_next;
54: reg [N-1:0] cnt_r;//
55:
56: reg [WIDTH-1:0] upper, lower;//楂樺崐鍜屼綆鍗
57: reg booth; //booth bit
58: reg [N-1:0] cnt;//
59: //reg [WIDTH_PROD-1:0] product;
60:
61: always @(posedge sys_clk or negedge sys_rst_n)
62: begin: MULTIPLICAND
63: if(!sys_rst_n)
64: begin
65: multiplicand_add <= 0;
66: multiplicand_minus <= 0;
67: end
68: else if(rfd)
69: begin
70: multiplicand_add <= multiplicand;
71: multiplicand_minus <= ~multiplicand + 1'b1;
72: end
73: end
74:
75: always @(posedge sys_clk or negedge sys_rst_n)
76: begin: STATE_CTRL
77: if(!sys_rst_n) begin
78: state_curr <= IDLE;
79: upper_r <= 0;
80: lower_r <= 0;
81: booth_r <=0;
82: cnt_r <= 0;
83: end
84: else begin
85: state_curr <= state_next;
86: upper_r <= upper;
87: lower_r <= lower;
88: booth_r <= booth;
89: cnt_r <= cnt;
90: end
91: end
92:
93: always @(*)
94: begin:STATE_NEXT
95: state_next = state_curr;
96: case(state_curr)
97: IDLE: begin
98: if(data_av)
99: state_next = ADD;
100: end
101: ADD:
102: state_next = SHIFT;
103: // TAP:
104: // state_next = SHIFT;
105: SHIFT: begin
106: if(cnt_r==WIDTH)
107: state_next = DONE;
108: else
109: state_next = ADD;
110: end
111: DONE:
112: state_next = IDLE;
113:
114: default: state_next = IDLE;
115: endcase
116:
117: end
118:
119: always @*
120: begin: OUT
121: rfd = 1'b0;
122: rdy = 1'b0;
123: product = 0;
124: cnt = cnt_r;
125: upper = upper_r;
126: lower = lower_r;
127: booth =booth_r;
128: case(state_curr)
129: IDLE: begin
130: rfd = 1'b1;
131: cnt = 0;
132: upper = 0;
133: booth = 1'b0;
134: if(data_av)
135: lower = multiplier;
136: end
137: ADD: begin
138: cnt = cnt_r + 1'b1;
139: case({lower_r[0],booth_r}) 140: 2'b00: upper = upper_r;
141: 2'b01: upper = upper_r + multiplicand_add;
142: 2'b10: upper = upper_r + multiplicand_minus;
143: 2'b11: upper = upper_r;
144:
145: endcase
146: end
147: //TAP: begin
148:
149: // end
150:
151: SHIFT: begin
152:
153:
154: upper = {upper_r[WIDTH-1],upper_r[WIDTH-1:1]}; 155: lower = {upper_r[0],lower_r[WIDTH-1:1]}; 156: booth = lower_r[0];
157:
158: end
159:
160: DONE: begin
161: product ={upper_r, lower_r}; 162: rdy = 1'b1;
163: end
164: endcase
165:
166: end
167:
168: always @(posedge sys_clk or negedge sys_rst_n)
169: begin: register
170: if(!sys_rst_n)
171: product_r <= 0;
172: else if(rdy)
173: product_r <= product;
174: end
175:
176: endmodule
177:
仿真结果
Do first what you dread the most.