The booth algorithm implements the multiplier

Source: Internet
Author: User

The booth algorithm takes full advantage of the importance of the complement, which allows us to reduce a lot of timing when we use the complement to calculate. The following table is an analysis of what we assume as a multiplier of 2. Next, I'll use the code to explain to you.

1, the beginning of the multiplier 2 of the ' negative one ' plus a default value of 0 00100
2, first judge [0:-1], the result is 2 ' b00, means ' 0 ' is no operation 00100
3. Judging [1:0] The result is 2 ' b10, which means ' 1 ' i.e. '-by multiplier ' operation 00100
4, Judge "2:1" result is 2 ' b10, means ' 1 ' is ' + by multiplier ' operation 00100
5, Judge "3:2" result is 2 ' b00, means ' 0 ' is no operation 00100

This test carries out two eight-digit multiplication operations.

[Email protected] (Posedge CLK or Negedge rst_n)
if (!rst_n)
Begin
I<=4 ' B0;
A<=8 ' B0;
B<=8 ' B0;
S<=8 ' B0;
P<=17 ' B0;
X<=4 ' B0;
Isdone<=1 ' B0;
End
else if (Start_sig)
Case (i)
0:
Begin
a<=a;
s<= (~a+1 ' B1);
P<={8 ' d0,b,1 ' B0};
I<=i+1 ' B1;
End
1:
if (x==8)
Begin
X<=4 ' D0;
I<=i+4 ' D2;
End
else if (p[1:0]==2 ' B01)
Begin
p<={p[16:9]+a,p[8:0]};
I<=i+1 ' B1;
End
else if (p[1:0]==2 ' B10)
Begin
p<={p[16:9]+s,p[8:0]};
I<=i+1 ' B1;
End
else I<=i+1 ' B1;
2:
Begin
p<={p[16],p[16:1]};
X<=x+1 ' B1;
I<=i+1 ' B1;
End
3:
Begin
Isdone<=1 ' B1;
I<=i+1 ' B1;
End
4:
Begin
I<=3 ' B0;
Isdone<=1 ' B0;
End
Endcase

The above is the core code, here we will be the multiplier A into two registers, a storage source data A, a storage complement s. Put the multiplier B into the P space for the shift operation.

Also set shift counter X to stop execution when 8 bits are reached. Otherwise, we will judge the last two bits of data if p[1:0] is 10, then p[16:9]+s, low eight-bit hold, if p[1:0]=01, then p[16:9]+a, low eight-bit hold. All the rest remained.

In the next step, the shift operation, the first is what to complement what, the data to move to the right. We can see the results by testing the files.

The booth algorithm implements the multiplier

Contact Us

The content source of this page is from Internet, which doesn't represent Alibaba Cloud's opinion; products and services mentioned on that page don't have any relationship with Alibaba Cloud. If the content of the page makes you feel confusing, please write us an email, we will handle the problem within 5 days after receiving your email.

If you find any instances of plagiarism from the community, please send an email to: info-contact@alibabacloud.com and provide relevant evidence. A staff member will contact you within 5 working days.

A Free Trial That Lets You Build Big!

Start building with 50+ products and up to 12 months usage for Elastic Compute Service

  • Sales Support

    1 on 1 presale consultation

  • After-Sales Support

    24/7 Technical Support 6 Free Tickets per Quarter Faster Response

  • Alibaba Cloud offers highly flexible support services tailored to meet your exact needs.