termux Why can't I run the program on SDcard?

u0_a238@localhost  ~/storage/external-1 # cat test.c
#include <stdio.h>

int main()
{
        printf("Hi!");
        return 0;
}
 u0_a238@localhost  ~/storage/external-1 # gcc test.c -o test
u0_a238@localhost  ~/storage/external-1 # ./test
zsh: permission denied: ./test
 ✘ u0_a238@localhost  ~/storage/external-1 # bash ./test
./test: ./test: cannot execute binary file
 ✘ u0_a238@localhost  ~/storage/external-1 # sh ./test
./test: 1: Syntax error: word unexpected (expecting ")")
u0_a238@localhost  ~/storage/external-1 # mv test ~
 u0_a238@localhost  ~/storage/external-1 # ~/test
Hi!%                                               u0_a238@localhost  ~/storage/external-1 # 

termux Why can't I run the program on SDcard? Is this Android's responsibility? Is there any way to get termux to execute the SDcard program? I want to build some programs from the source code and install them on SDcard Or install the APK directly on the SDcard Is there any other way besides root?

See the Termux documentation.

Unfortunately, SD cards are considered external storage and do not support executables.

You need to copy your project or executable to a $HOME subfolder.