About algorithm change the number you can see on the net, however, the program would be the change of system 10 to Us 2, 8, 16 and in accordance with the format we still do.
Perform on dev-C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>
#include <windows.h>
#define d 179//186
#define ng 196//205
#define gi 197//206
#define swap(type, a, b) {type temp = a; a= b; b =temp;}
void gotoxy(int x, int y)	// chuyen con tro toi (x,y)
{
	static HANDLE h = NULL; 
	if(!h)
		h = GetStdHandle(STD_OUTPUT_HANDLE);
	COORD c = { x, y }; 
	SetConsoleCursorPosition(h,c);
}

void reverse(char s[])		// dao nguoc xau
{
	int i;
	for (i=0; i<strlen(s)/2; i++)
		swap(char, s[i], s[strlen(s)-i - 1]);
}

int main()
{
	int a, n;
	int x, y = 3, sys, i, l1, l2, count;
	char s1[100], s2[100], s[100], result[1000];
	char again;	
	char *syschar = (char*) malloc(20*sizeof(char));
	begin:
	x = 4, sys = 2, i, l1 = 0, l2 = 0, count =0;
	printf("Enter number want convert : ");
	scanf("%d", &n);
	a = n;
	do
	{
		printf("Enter number system (2,8,16): ");
		scanf("%d", &sys);
	}while (sys != 2 && sys != 8 && sys != 16);
	if (sys == 2) strcpy(syschar, "01"); //syschar = "01";
	else if (sys == 8) strcpy(syschar, "01234567");
	else if (sys == 16) strcpy(syschar, "0123456789ABCDEF");

	gotoxy(x, y);
	printf("%d",n);
	while (n>0)
	{
		sprintf(s1,"%-2d", n);				// chuyen n sang xau s1
		sprintf(s2,"%-2d",n/sys);			// chuyen n/sys sang xau s2
		result[count] = syschar[n%sys];	// cong phan du vao kq
		l1 = strlen(s1);					
		l2 = strlen(s2);
		gotoxy(x + l1, y);		
		printf(" %c %d",d, sys);		// in | va co so
		gotoxy(2, ++y);	
		if (count>0) printf("%c", d);	// in mu ten
		gotoxy(x, y);
		for (i=0; i<l1 + 3 + l2; i++)	// in -------
			if (i==l1+1) printf("%c", gi);
			else printf("%c", ng);
		gotoxy(2, ++y);	
		if (count==0) printf("%c",30);	// in duong thang dung cua mui ten
		else printf("%c", d);
		gotoxy(x, y);
		for (i = 0; i<l1-2; i++)		// in khoang trong truoc so du
			printf(" ");
		sprintf(s,"%-2d %c %s", n%sys, d, s2);	// in so du va thuong
		printf("%-2d %c %s", n%sys, d, s2);
		x += l1-2 + strlen(s) - l2; 			// tang x den vi tri moi
		n /=sys;
		count++;
	}
	y+=7;
	result[count] = '\0';
	reverse(result);
	printf("nn%d(10) = %s(%d)",a, result, sys);
	printf("nDo you want continue? (y/n)");
	fflush(stdin);
	again = getchar();
	again = toupper(again);
	if (again == 'Y') goto begin;
	free(syschar);
	return 0;
}

Implementation on Linux terminal

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <ctype.h>
#define d 124//179//186
#define ng 45//196//205
#define gi 124//197//206
#define gotoxy(type, x, y) printf("%c[%d;%df",0x1B,x, y)
#define swap(type, a, b) {type temp = a; a= b; b =temp;}
void reverse(char s[])		// dao nguoc xau
{
	int i, l = strlen(s)/2;
	for (i=0; i<l; i++)
		swap(char, s[i], s[strlen(s)-i - 1]);
}

int main()
{
	int a, n;
	int x = 4, y, sys, i, l1, l2, count;
	char s1[100], s2[100], s[100], result[1000];
	char again;	
	char *syschar = (char*) malloc(20*sizeof(char));
	do
	{
		y = 5; sys = 2; l1 = 0; l2 = 0; count =0;
		printf("Enter number want convert : ");
		scanf("%d", &n);
		a = n;
		do
		{
			printf("Enter number system (2,8,16): ");
			scanf("%d", &sys);
		}while (sys != 2 && sys != 8 && sys != 16);
		if (sys == 2) strcpy(syschar, "01"); //syschar = "01";
		else if (sys == 8) strcpy(syschar, "01234567");
		else if (sys == 16) strcpy(syschar, "0123456789ABCDEF");
		
		gotoxy(int, x, y);
		printf("%d",n);
		while (n>0)
		{
			sprintf(s1,"%-2d", n);				// chuyen n sang xau s1
			sprintf(s2,"%-2d",n/sys);			// chuyen n/sys sang xau s2
			result[count] = syschar[n%sys];	// cong phan du vao kq
			l1 = strlen(s1);					
			l2 = strlen(s2);
			gotoxy(int, x , y + l1);		
			printf(" %c %d",d, sys);		// in | va co so
			gotoxy(int, ++x, 2);	
			if (count>0) printf("%c", d);	// in mu ten
			gotoxy(int, x, y);
			for (i=0; i<l1 + 3 + l2; i++)	// in -------
				if (i==l1+1) printf("%c", gi);
				else printf("%c", ng);
			gotoxy(int, ++x, 2);	
			if (count==0) printf("%c",'^');	// in duong thang dung cua mui ten
			else printf("%c", d);
			gotoxy(int, x, y);
			for (i = 0; i<l1-2; i++)		// in khoang trong truoc so du
				printf(" ");
			sprintf(s,"%-2d %c %s", n%sys, d, s2);	// in so du va thuong
			printf("%-2d %c %s", n%sys, d, s2);
			y += l1-2 + strlen(s) - l2; 			// tang x den vi tri moi
			n /=sys;
			count++;
		}
		x += 7;
		result[count] = '\0';
		reverse(result);
		printf("nn%d(10) = %s(%d)",a, result, sys);
		printf("nDo you want continue? (y/n)");
		fgets (s,256,stdin);
		scanf("%c", &again);
		again = toupper(again);
	}while (again == 'Y');// goto begin;
	return 0;
}

Read more:
Principles to switch between the base system
Show us some 2, Contacts 8, Contacts 16 of decimal