今天重新补习了一下二进制原码，反码和补码之间的关系以及正数变负数，负数变正数之间的关系。瞬间感觉好晕，赶紧仔细研究：
原码就是符号位加上真值的绝对值。正数原码是其本身，负数符号位为1.
正数的反码和补码都是其本身，负数反码为符号位不变，其余各位依次取反；补码为符号位不变，其余各位依次取反后加1。
这都好理解，那一个正数怎么变为负数呢？
注意计算机内存储负数是其补码形式！ 正数取反后加1就得到负数（其实是负数的补码），例如：7二进制为0111；取反后为1000；然后+1为1001=（-7）补码。
同理负数取反+1后得到正数的补码=正数本身。
好了理清了上述关系 下面实现一个booth算法乘法器：
booth算法其实就是一种位操作，直接上例子
| bit[1] |
bit[2] |
位操作 |
| 0 |
0 |
无操作 |
| 0 | 1 | +被乘数 |
| 1 |
0 |
-被乘数 |
| 1 | 1 | 无操作 |
例如4*2 被乘数为4（0100），乘数为2（0010），都为4bit，因此result应有9bit空间。
第一步：被乘数正数：0100 负数为：1100，result={4’d0,0010,0}
第二步：判断result[1:0] ,为00 则无操作，result向右移一位，补高位与原来高位一致为result={4’d0,0001，0}
第三步：判断result[1:0],为10则减被乘数，result[9:6]+4’b1100={1100,0001,0}，result向右移一位，高位补1，result={1110,0000,1}
第四步：判断result[1:0],为01则加被乘数，result[9:6]+4’b0100={0010,0000,1}，result向右移一位，高位补0，result={0001,0000,0}
第五步：判断result[1:0],为00则无操作，result向右移一位，高位补0，result={0000,0001,0}
第六步：最后结果取result[9:1]={0000,1000}=8;
中间判断次数为寄存器宽度，即4bit执行4次，然后去高8为最后结果。
下面为位宽8bit的booth乘法器verilog代码：
//----------------------------------------------------------------------------- // Title : <title> // Project : <project> //----------------------------------------------------------------------------- // File : multiplier.v // Author : caoshan // Created : <credate> // Last modified : <moddate> //----------------------------------------------------------------------------- // Description : // <description> //----------------------------------------------------------------------------- // Copyright (c) <copydate> by <company> This model is the confidential and // proprietary property of <company> and the possession or use of this // file requires a written license from <company>. //------------------------------------------------------------------------------ // Modification history : // <modhist> //----------------------------------------------------------------------------- module multiplier(/*autoarg*/ // Outputs done_flag, mul_result, // Inputs clk, rst_n, start_en, mul_cand_data, mul_data ); // parameter WIDTH = 8; //system interface input clk; input rst_n; input start_en; input [7:0] mul_cand_data; input [7:0] mul_data; output done_flag; output [15:0] mul_result; /*autoinput*/ /*autooutput*/ /*autoreg*/ // Beginning of automatic regs (for this module's undeclared outputs) reg done_flag; //reg [2*WIDTH-1:0] mul_result; // End of automatics /*autowire*/ //=========================================================== // state machine //======================================================= parameter IDLE = 3'd0; parameter LOCK_DATA = 3'd1; parameter IMPROVE_MC = 3'd2; parameter IMPROVE_M = 3'd3; parameter JUDGE = 3'd4; parameter MUL_MOV = 3'd5; parameter MUL_END = 3'd6; reg [2:0] curr_state; reg [2:0] next_state; reg [7:0] mul_cand_data_ff1; reg [7:0] mul_cand_data_ff2; reg [7:0] mul_data_ff; reg [16:0] mul_result_ff; reg [7:0] cnt; always @ (posedge clk or negedge rst_n)begin if(rst_n == 0) curr_state <= IDLE; else curr_state <= next_state; end always @ (*)begin next_state = IDLE; case(curr_state) IDLE:begin if(start_en) next_state = LOCK_DATA; else next_state = IDLE; end LOCK_DATA:begin next_state = IMPROVE_MC; end IMPROVE_MC:begin next_state = IMPROVE_M; end IMPROVE_M:begin next_state = JUDGE; end JUDGE:begin next_state = MUL_MOV; end MUL_MOV:begin if(cnt >= 7) next_state = MUL_END; else next_state = JUDGE; end MUL_END:begin next_state = IDLE; end default: next_state = IDLE; endcase // case (curr_state) end // always @ (*) //------------------------------------- //state machine change always@(posedge clk or negedge rst_n)begin if(rst_n==0)begin mul_cand_data_ff1 <= 0; mul_cand_data_ff2 <= 0; mul_data_ff <= 0; end else if(curr_state == IMPROVE_MC)begin mul_cand_data_ff1 <= mul_cand_data; mul_cand_data_ff2 <= ~mul_cand_data + 1'b1; mul_data_ff <= mul_data; end end always @ (posedge clk or negedge rst_n)begin if(rst_n == 0) mul_result_ff <= 0; else if(curr_state == IMPROVE_M) mul_result_ff <= {8'd0,mul_data_ff,1'b0}; else if(curr_state == JUDGE)begin if(mul_result_ff[1:0]==2'b01) mul_result_ff <= {(mul_result_ff[16:9] + mul_cand_data_ff1[7:0]),mul_result_ff[8:0]}; else if(mul_result_ff[1:0]== 2'b10) mul_result_ff <= {(mul_result_ff[16:9] + mul_cand_data_ff2[7:0]),mul_result_ff[8:0]}; end else if(curr_state == MUL_MOV) mul_result_ff <= {mul_result_ff[16],mul_result_ff[16:1]}; end // always @ (posedge clk or negedge rst_n) always @ (posedge clk or negedge rst_n)begin if(rst_n == 0) cnt <= 0; else if((curr_state == MUL_MOV)&&(cnt < 7)) cnt <= cnt + 1'b1; else if((cnt >=7 )&&(curr_state == MUL_END)) cnt <= 0; end always@(posedge clk or negedge rst_n)begin if(rst_n == 0) done_flag <= 0; else if(curr_state == MUL_END) done_flag <= 1; else done_flag <= 0; end reg[16:0] mul_result_ff2; always @ (posedge clk or negedge rst_n)begin if(rst_n == 0) mul_result_ff2 <= 0; else if(curr_state == MUL_END) mul_result_ff2 <= mul_result_ff; end assign mul_result = mul_result_ff2[16:1]; endmodule //
testbench：
//----------------------------------------------------------------------------- // Title : <title> // Project : <project> //----------------------------------------------------------------------------- // File : test_bench.v // Author : cs // Created : <credate> // Last modified : <moddate> //----------------------------------------------------------------------------- // Description : // <description> //----------------------------------------------------------------------------- // Copyright (c) <copydate> by <company> This model is the confidential and // proprietary property of <company> and the possession or use of this // file requires a written license from <company>. //------------------------------------------------------------------------------ // Modification history : // <modhist> //----------------------------------------------------------------------------- module testbench(); reg clk; reg rst_n; reg start_en; reg [7:0] mul_cand_data; reg [7:0] mul_data; wire done_flag; wire [15:0] mul_result; //------------------------------------------------------------------------------ multiplier u_multiplier(/*autoinst*/ // Outputs .done_flag (done_flag), .mul_result (mul_result[15:0]), // Inputs .clk (clk), .rst_n (rst_n), .start_en (start_en), .mul_cand_data (mul_cand_data[7:0]), .mul_data (mul_data[7:0])); always #20 clk = ~clk; initial begin clk = 0; rst_n = 0; # 100 rst_n = 1; end reg [3:0] i; always@(posedge clk or negedge rst_n)begin if(rst_n==0)begin start_en <= 0; mul_cand_data <= 0; mul_data <= 0; i <= 0; end else case(i) 0:begin if(done_flag)begin start_en = 0; i <= i + 1'b1; end else begin start_en <= 1'b1; mul_cand_data <= 8'd5; mul_data <= 8'd8; end end // case: 0 1:begin if(done_flag)begin start_en = 0; i <= i + 1'b1; end else begin start_en <= 1'b1; mul_cand_data <= 8'b11111100; mul_data <= 8'd4; end end // case: 1 2:begin if(done_flag)begin start_en = 0; i <= i + 1'b1; end else begin start_en <= 1'b1; mul_cand_data <= 8'd127; mul_data <= 8'b10000001; end end // case: 2 3:begin if(done_flag)begin start_en = 0; i <= i + 1'b1; end else begin start_en <= 1'b1; mul_cand_data <= 8'b10000001; mul_data <= 8'b10000001; end end // case: 3 4:begin i<=4'd4;
mul_cand_data <= 0;
mul_data <= 0;
end endcase // case (i) end // always@ (posedge clk or negedge rst_n) initial begin $fsdbDumpfile ("./testbench.fsdb"); $fsdbDumpvars; // end endmodule
仿真结果
2015年4月9日
cslegend