10 進数と符号付き 2 進固定小数点 10 進変換の MATLAB コード
この MATLAB コードを書いたのは、FPGA のコンテストを行っていたときでした.理由は、FPGA で多くの固定小数点 10 進数の計算に遭遇し、手動の形式変換が面倒だったため、コードで解決したからです.
1. 10 進数を 2 進数に変換します。
clc;
clear;
integer = 4; %整数位数
decimal = 14; %小数位数
sum_before_point = 0;
sum_after_point = 0;
sum = 0;
before_point_arr = zeros(1, integer + 1);
after_point_arr = zeros(1, decimal);
while (1)
prompt = 'What is the deciaml value? ';
num = input(prompt);
lenrth_data = length(num);
%------------------------------%
if (num < 0)
before_point_arr(integer + 1) = 1;
num = abs(num);
flag = 1;
else
before_point_arr(integer + 1) = 0;
flag = 0;
end
%------------------------------%
before_point = fix(num);
for i = 1:integer
before_point_arr(i) = mod(before_point, 2);
before_point = fix(before_point / 2);
if (before_point <= 1)
before_point_arr(i + 1) = before_point;
break;
end
end
%------------------------------%
after_point = num - fix(num);
for j = 1:decimal
after_point_arr(j) = fix(after_point * 2);
after_point = after_point * 2;
if (after_point >= 1)
after_point = after_point - 1;
end
end
%------------------------------%
if (flag == 1)
for i = 1:integer
switch (before_point_arr(i))
case 0
before_point_arr(i) = 1;
case 1
before_point_arr(i) = 0;
end
end
for k = 1:integer
before_point_arr(k) = before_point_arr(k) + 1;
if (before_point_arr(k) == 1)
break;
else if(before_point_arr(k) == 2)
before_point_arr(k) = 0;
end
end
end
for j = 1:decimal
switch (after_point_arr(j))
case 0
after_point_arr(j) = 1;
case 1
after_point_arr(j) = 0;
end
end
end
%------------------------------%
if (flag == 1)
fprintf('%d', 1);
else if(flag == 0)
fprintf('%d', 0);
end
end
for i = 1:integer
fprintf('%d', before_point_arr(integer + 1 - i));
end
for j = 1:decimal
fprintf('%d', after_point_arr(j));
end
fprintf('\n');a
%------------------------------%
before_point_arr = 0;
after_point_arr = 0;
flag = 0;
end
説明: 出力 2 進固定小数点 10 進数の最上位ビット (左端のビット) は符号ビットです。
上の図に示すように、10 進数を直接入力することができ、出力結果は一連の連続した 0 と 1 であり、4 つの整数ビットを設定したため、丸印が最上位の符号ビットであるため、端子ボックスは整数ビットなので、2 進数の総数は 1+4+14=19 ビットです。
2. 2 進数を 10 進数に変換する
clc;
clear;
format long g;
%正数原码位数限制integer + decimal < 23,负数补码位数限制integer + decimal < 16
integer = 1; %整数位数
decimal = 21; %小数位数
sum_before_point = 0;
sum_after_point = 0;
sum = 0;
while (1)
prompt = 'What is the binary value? ';
num = input(prompt);
lenrth_data = length(num);
before_point_arr = zeros(1, integer + 1);
after_point_arr = zeros(1, decimal);
%------------------------------%
tempt = num;
z = 10.^decimal;
tempt = tempt / z;
for i = 1:integer + 1
before_point_arr(i) = fix(mod(tempt, 10));
tempt = tempt / 10;
end
if (before_point_arr(integer + 1) == 1)
flag = 1;
else
flag = 0;
end
%------------------------------%
if(mod(decimal, 2))
odd = 1;
else
odd = 0;
end
if(odd)
x = (decimal - 1) / 2;
y = (decimal + 1) / 2;
z = 10.^x;
tempt = fix(mod(num, z));
for j = 1:x
after_point_arr(j) = fix(mod(tempt, 10));
tempt = tempt / 10;
end
tempt = num / z;
for j = y:decimal
after_point_arr(j) = fix(mod(tempt, 10));
tempt = tempt / 10;
end
else
x = decimal / 2;
y = x + 1;
z = 10.^x;
tempt = mod(fix(num), z);
for j = 1:x
after_point_arr(j) = mod(fix(tempt), 10);
tempt = tempt / 10;
end
tempt = num / z;
for j = y:decimal
after_point_arr(j) = mod(fix(tempt), 10);
tempt = tempt / 10;
end
end
%------------------------------%
if (flag == 1)
for i = 1:integer
switch (after_point_arr(i))
case 0
before_point_arr(i) = 1;
case 1
before_point_arr(i) = 0;
end
end
for k = 1:integer
before_point_arr(k) = before_point_arr(k) + 1;
if (before_point_arr(k) == 1)
break;
else if (before_point_arr(k) == 2)
before_point_arr(k) = 0;
end
end
end
for j = 1:decimal
switch (after_point_arr(j))
case 0
after_point_arr(j) = 1;
case 1
after_point_arr(j) = 0;
end
end
end
%------------------------------%
for i = 1:integer
sum_before_point = sum_before_point + before_point_arr(i) * 2.^(i - 1);
end
for j = 1:decimal
sum_after_point = sum_after_point + after_point_arr(j) * 2.^(j - decimal - 1);
end
sum = sum_before_point + sum_after_point;
if (flag == 1)
sum = -sum;
end
%------------------------------%
disp(sum);
flag = 0;
sum = 0;
sum_before_point = 0;
sum_after_point = 0;
before_point_arr = 0;
after_point_arr = 0;
end
解説:MATLABのモジュロ関数はmod
桁数制限があるため、入力する2進数の桁数にも制限があります.
上図のように、入力の際は2進数の0と1の文字列を直接入力しますが、桁数の制限に注意してください.正数と負数の桁数。