兩個N位二進制數x、y的乘積用簡單的方法計算就是利用移位操作來實作。
![](https://img.laitimes.com/img/9ZDMuAjOiMmIsIjOiQnIsISPrdEZwZ1Rh5WNXp1bwNjW1ZUba9VZwlHdsATOfd3bkFGazxCMx8VesATMfhHLlN3XnxCMwEzX0xiRGZkRGZ0Xy9GbvNGLpZTY1EmMZVDUSFTU4VFRR9Fd4VGdsYTMfVmepNHLrJXYtJXZ0F2dvwVZnFWbp1zczV2YvJHctM3cv1Ce-YWan5SMyAzY3EGM3ETMhVmYjNWMycDZjVWNxATOxEjYjJTZm9CXxMzLcdDMxIDMy8CXn9Gbi9CXzV2Zh1WavwVbvNmLvR3YxUjL0M3Lc9CX6MHc0RHaiojIsJye.gif)
module multi_CX(clk, x, y, result);
input clk;
input [7:0] x, y;
output [15:0] result;
reg [15:0] result;
parameter s0 = 0, s1 = 1, s2 = 2;
reg [2:0] count = 0;
reg [1:0] state = 0;
reg [15:0] P, T;
reg [7:0] y_reg;
always @(posedge clk) begin
case (state)
s0: begin
count <= 0;
P <= 0;
y_reg <= y;
T <= {{8{1'b0}}, x};
state <= s1;
end
s1: begin
if(count == 3'b111)
state <= s2;
else begin
if(y_reg[0] == 1'b1)
P <= P + T;
else
P <= P;
y_reg <= y_reg >> 1;
T <= T << 1;
count <= count + 1;
state <= s1;
end
end
s2: begin
result <= P;
state <= s0;
end
default: ;
endcase
end
endmodule
![](https://img.laitimes.com/img/9ZDMuAjOiMmIsIjOiQnIsISPrdEZwZ1Rh5WNXp1bwNjW1ZUba9VZwlHdsATOfd3bkFGazxCMx8VesATMfhHLlN3XnxCMwEzX0xiRGZkRGZ0Xy9GbvNGLpZTY1EmMZVDUSFTU4VFRR9Fd4VGdsYTMfVmepNHLrJXYtJXZ0F2dvwVZnFWbp1zczV2YvJHctM3cv1Ce-YWan5SMyAzY3EGM3ETMhVmYjNWMycDZjVWNxATOxEjYjJTZm9CXxMzLcdDMxIDMy8CXn9Gbi9CXzV2Zh1WavwVbvNmLvR3YxUjL0M3Lc9CX6MHc0RHaiojIsJye.gif)
乘法功能是正确的,但計算一次乘法須要8個周期。是以能夠看出串行乘法器速度比較慢、時延大。但這樣的乘法器的長處是所占用的資源是全部類型乘法器中最少的,在低速的信号進行中有着廣泛的應用。
2.流水線乘法器
一般的高速乘法器通常採用逐位并行的疊代陣列結構,将每一個操作數的N位都并行地送出給乘法器。可是一般對于FPGA來講。進位的速度快于加法的速度,這樣的陣列結構并非最優的。是以能夠採用多級流水線的形式。将相鄰的兩個部分乘積結果再加到終于的輸出乘積上,即排成一個二叉樹形式的結構,這樣對于N位乘法器須要lb(N)級來實作。
![](https://img.laitimes.com/img/9ZDMuAjOiMmIsIjOiQnIsISPrdEZwZ1Rh5WNXp1bwNjW1ZUba9VZwlHdsATOfd3bkFGazxCMx8VesATMfhHLlN3XnxCMwEzX0xiRGZkRGZ0Xy9GbvNGLpZTY1EmMZVDUSFTU4VFRR9Fd4VGdsYTMfVmepNHLrJXYtJXZ0F2dvwVZnFWbp1zczV2YvJHctM3cv1Ce-YWan5SMyAzY3EGM3ETMhVmYjNWMycDZjVWNxATOxEjYjJTZm9CXxMzLcdDMxIDMy8CXn9Gbi9CXzV2Zh1WavwVbvNmLvR3YxUjL0M3Lc9CX6MHc0RHaiojIsJye.gif)
module multi_4bits_pipelining(mul_a, mul_b, clk, rst_n, mul_out);
input [3:0] mul_a, mul_b;
input clk;
input rst_n;
output [7:0] mul_out;
reg [7:0] mul_out;
reg [7:0] stored0;
reg [7:0] stored1;
reg [7:0] stored2;
reg [7:0] stored3;
reg [7:0] add01;
reg [7:0] add23;
always @(posedge clk or negedge rst_n) begin
if(!rst_n) begin
mul_out <= 0;
stored0 <= 0;
stored1 <= 0;
stored2 <= 0;
stored3 <= 0;
add01 <= 0;
add23 <= 0;
end
else begin
stored0 <= mul_b[0]? {4'b0, mul_a} : 8'b0;
stored1 <= mul_b[1]? {3'b0, mul_a, 1'b0} : 8'b0;
stored2 <= mul_b[2]? {2'b0, mul_a, 2'b0} : 8'b0;
stored3 <= mul_b[3]? {1'b0, mul_a, 3'b0} : 8'b0;
add01 <= stored1 + stored0;
add23 <= stored3 + stored2;
mul_out <= add01 + add23;
end
end
endmodule
![](https://img.laitimes.com/img/9ZDMuAjOiMmIsIjOiQnIsISPrdEZwZ1Rh5WNXp1bwNjW1ZUba9VZwlHdsATOfd3bkFGazxCMx8VesATMfhHLlN3XnxCMwEzX0xiRGZkRGZ0Xy9GbvNGLpZTY1EmMZVDUSFTU4VFRR9Fd4VGdsYTMfVmepNHLrJXYtJXZ0F2dvwVZnFWbp1zczV2YvJHctM3cv1Ce-YWan5SMyAzY3EGM3ETMhVmYjNWMycDZjVWNxATOxEjYjJTZm9CXxMzLcdDMxIDMy8CXn9Gbi9CXzV2Zh1WavwVbvNmLvR3YxUjL0M3Lc9CX6MHc0RHaiojIsJye.gif)
從圖中能夠看出,流水線乘法器比串行乘法器的速度快非常多非常多,在非快速的信号進行中有廣泛的應用。至于快速信号的乘法一般須要利用FPGA晶片中内嵌的硬核DSP單元來實作。