diff --git a/conversions/binary_to_decimal.c b/conversions/binary_to_decimal.c
index 352d07c16..7431995a7 100644
--- a/conversions/binary_to_decimal.c
+++ b/conversions/binary_to_decimal.c
@@ -1,24 +1,104 @@
+/** 
+ * @file
+ * @brief Converts a [binary number to a decimal](https://byjus.com/binary-to-decimal-formula/) number.
+ * @details
+ * A binary number is an input that is checked to be binary
+ * then, the number is converted to a decimal number.
+ * @author [Kyler Smith](https://github.com/KylerSmith)
+ * @author [lazy-dude](https://github.com/lazy-dude)
+ */
+
+#include <assert.h>     /// for assert
+#include <stdbool.h>   /// for bool
+#include <stdint.h>   /// for uintmax_t
+#include <stdio.h>   /// for IO operations
+
 /**
- * Modified 07/12/2017, Kyler Smith
- *
+ * @brief checks whether the number is binary
+ * @param num the number to be checked if it has binary representation
+ * @returns `true` if the number IS binary
+ * @returns `false` if the number is NOT binary
  */
+bool is_binary(uintmax_t num)
+{
+    unsigned remainder = 0;
 
-#include <stdio.h>
+    while (num > 0) {
+        remainder = num % 10;
+        // make sure each digit is 0 or 1
+        if (remainder == 0 || remainder == 1) {
+            num /= 10;
+            continue;
+        } else
+            return false;
+    }
+    return true;
+}
 
-int main()
+/**
+ * @brief finds the length of an `uintmax_t` number
+ * @param num whose length to be computed
+ * @returns the length of the number
+ */
+uint16_t num_len(uintmax_t num)
 {
-    int remainder, number = 0, decimal_number = 0, temp = 1;
-    printf("\n Enter any binary number= ");
-    scanf("%d", &number);
-
-    // Iterate over the number until the end.
-    while (number > 0)
-    {
-        remainder = number % 10;
-        number = number / 10;
-        decimal_number += remainder * temp;
-        temp = temp * 2;  // used as power of 2
+    uint16_t len = 0;
+    for (len = 0; num > 0; len++) {
+        num /= 10;
     }
+    return len;
+}
+
+/**
+ * @brief The `binary_decimal` function does the actual job of conversion
+ * @param number the number binary to be converted
+ * @returns decimal_number decimal representation of a binary number
+ */
+uintmax_t binary_decimal(uintmax_t number)
+{
+	uint8_t remainder;
+	uintmax_t decimal_number = 0;
+	uint32_t temp = 1;
 
-    printf("%d\n", decimal_number);
+	uint16_t length = num_len(UINTMAX_MAX) - 1;
+    
+	assert(num_len(number) <= length);
+	assert(is_binary(number));
+
+	// Iterate over the number until the end.
+	while (number > 0) {
+		remainder = number % 10;
+		number = number / 10;
+		decimal_number += remainder * temp;
+		temp = temp * 2; // used as power of 2
+	}
+
+	return decimal_number;
+}
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test()
+{
+	assert(binary_decimal(0)==0);
+	assert(binary_decimal(1)==1);
+	assert(binary_decimal(1110001)==113);
+	assert(binary_decimal(11111111)==255);
+	assert(binary_decimal(10000000000)==1024);
+	assert(binary_decimal(1001110100000100)==40196);
+
+        printf("All tests have passed!\n");
+}
+
+/**
+ * @brief main function
+ * @param void
+ * @returns 0 on exit
+ */
+int main()
+{
+    test();  // run self-test implementations
+    return 0;
 }
diff --git a/conversions/decimal_to_hexa.c b/conversions/decimal_to_hexa.c
index 89de59623..dbf5184c5 100644
--- a/conversions/decimal_to_hexa.c
+++ b/conversions/decimal_to_hexa.c
@@ -18,6 +18,7 @@ int main()
  * number****************/
 void decimal2Hexadecimal(long num)
 {
+	char hex_letters[]="abcdef";
     long decimalnum = num;
     long quotient, remainder;
     int i, j = 0;
@@ -29,17 +30,17 @@ void decimal2Hexadecimal(long num)
     {
         remainder = quotient % 16;
         if (remainder < 10)
-            hexadecimalnum[j++] = 48 + remainder;
+            hexadecimalnum[j++] = '0' + remainder;
 
         else
-            hexadecimalnum[j++] = 55 + remainder;
+            hexadecimalnum[j++] =  hex_letters[remainder-10];// 'A'
 
         quotient = quotient / 16;
     }
 
     // print the hexadecimal number
-
-    for (i = j; i >= 0; i--)
+	printf("0x");
+    for (i = j-1; i >= 0; i--)
     {
         printf("%c", hexadecimalnum[i]);
     }