diff --git a/src/hardware/cpu/mmu.c b/src/hardware/cpu/mmu.c
index 9e7f4a9..d701903 100644
--- a/src/hardware/cpu/mmu.c
+++ b/src/hardware/cpu/mmu.c
@@ -17,10 +17,13 @@
 #include "headers/common.h"
 #include "headers/address.h"
 
+static uint64_t page_walk(uint64_t vaddr_value);
+
 // consider this function va2pa as functional
 uint64_t va2pa(uint64_t vaddr)
 {
     // use page table as va2pa
+    return page_walk(vaddr);
 }
 
 // input - virtual address
@@ -30,9 +33,109 @@ static uint64_t page_walk(uint64_t vaddr_value)
     address_t vaddr = {
         .vaddr_value = vaddr_value
     };
+    int page_table_size = PAGE_TABLE_ENTRY_NUM * sizeof(pte123_t);  // should be 4KB
 
     // CR3 register's value is malloced on the heap of the simulator
     pte123_t *pgd = (pte123_t *)cpu_controls.cr3;
+    assert(pgd != NULL);
+    
+    if (pgd[vaddr.vpn1].present == 1)
+    {
+        // PHYSICAL PAGE NUMBER of the next level page table
+        // aka. high bits starting address of the page table
+        pte123_t *pud = pgd[vaddr.vpn1].paddr;
+
+        if (pud[vaddr.vpn2].present == 1)
+        {
+            // find pmd ppn
+
+            pte123_t *pmd = (pte123_t *)(pud[vaddr.vpn2].paddr);
+
+            if (pmd[vaddr.vpn3].present == 1)
+            {
+                // find pt ppn
+                
+                pte4_t *pt = (pte4_t *)(pmd[vaddr.vpn3].paddr);
+
+                if (pt[vaddr.vpn4].present == 1)
+                {
+                    // find page table entry
+                    address_t paddr = {
+                        .ppn = pt[vaddr.vpn4].ppn,
+                        .ppo = vaddr.vpo    // page offset inside the 4KB page
+                    };
+
+                    return paddr.paddr_value;
+                }
+                else
+                {
+                    // page table entry not exists
+#ifdef DBUEG_PAGE_WALK
+                    printf("page walk level 4: pt[%lx].present == 0\n\tmalloc new page table for it\n", vaddr.vpn1);
+#endif
+                    pte4_t *pt = malloc(page_table_size);
+                    memset(pt, 0, page_table_size);
+
+                    // set page table entry
+                    pmd[vaddr.vpn3].present = 1;
+                    pud[vaddr.vpn3].paddr   = (uint64_t)pt;
+
+                    // TODO: page fault here
+                    // map the physical page and the virtual page
+                    exit(0);
+                }
+            }
+            else
+            {
+                // pt - level 4 not exists
+#ifdef DBUEG_PAGE_WALK
+                printf("page walk level 3: pmd[%lx].present == 0\n\tmalloc new page table for it\n", vaddr.vpn1);
+#endif
+                pte4_t *pt = malloc(page_table_size);
+                memset(pt, 0, page_table_size);
+
+                // set page table entry
+                pmd[vaddr.vpn3].present = 1;
+                pud[vaddr.vpn3].paddr   = (uint64_t)pt;
+
+                // TODO: page fault here
+                // map the physical page and the virtual page
+                exit(0);
+            }
+        }
+        else
+        {
+            // pmd - level 3 not exists
+#ifdef DBUEG_PAGE_WALK
+            printf("page walk level 2: pud[%lx].present == 0\n\tmalloc new page table for it\n", vaddr.vpn1);
+#endif
+            pte123_t *pmd = malloc(page_table_size);
+            memset(pmd, 0, page_table_size);
+
+            // set page table entry
+            pud[vaddr.vpn2].present = 1;
+            pud[vaddr.vpn2].paddr   = (uint64_t)pmd;
+
+            // TODO: page fault here
+            // map the physical page and the virtual page
+            exit(0);
+        }
+    }
+    else
+    {
+        // pud - level 2 not exists
+#ifdef DBUEG_PAGE_WALK
+        printf("page walk level 1: pgd[%lx].present == 0\n\tmalloc new page table for it\n", vaddr.vpn1);
+#endif
+        pte123_t *pud = malloc(page_table_size);
+        memset(pud, 0, page_table_size);
+
+        // set page table entry
+        pgd[vaddr.vpn1].present = 1;
+        pgd[vaddr.vpn1].paddr   = (uint64_t)pud;
 
-    pte123_t *pmd = (pte123_t *)(pgd[vaddr.vpn1].paddr);
+        // TODO: page fault here
+        // map the physical page and the virtual page
+        exit(0);
+    }
 }
\ No newline at end of file
diff --git a/src/headers/memory.h b/src/headers/memory.h
index 276a0de..45ff6f0 100644
--- a/src/headers/memory.h
+++ b/src/headers/memory.h
@@ -23,8 +23,10 @@
 // in this simulator, there are 4 + 6 + 6 = 16 bit physical adderss
 // then the physical space is (1 << 16) = 65536
 // total 16 physical memory
-#define PHYSICAL_MEMORY_SPACE   65536
-#define MAX_INDEX_PHYSICAL_PAGE 15
+#define PHYSICAL_MEMORY_SPACE   (65536)
+#define MAX_INDEX_PHYSICAL_PAGE (15)
+
+#define PAGE_TABLE_ENTRY_NUM    (512)
 
 // physical memory
 // 16 physical memory pages