diff --git a/src/boot/memory_map.cpp b/src/boot/memory_map.cpp
index afbc6be..eebcfa9 100644
--- a/src/boot/memory_map.cpp
+++ b/src/boot/memory_map.cpp
@@ -249,13 +249,13 @@ build_frame_blocks(const util::counted<bootproto::mem_entry> &kmap)
                 unsigned i = 0;
 
                 uint64_t b1 = (page_count + 4095) / 4096;
-                blk->map1 = (1 << b1) - 1;
+                blk->map1 = (1ull << b1) - 1;
 
                 uint64_t b2 = (page_count + 63) / 64;
                 uint64_t b2q = b2 / 64;
                 uint64_t b2r = b2 % 64;
                 g_alloc.memset(blk->map2, b2q, 0xff);
-                blk->map2[b2q] = (1 << b2r) - 1;
+                blk->map2[b2q] = (1ull << b2r) - 1;
                 break;
             }
         }
@@ -269,7 +269,7 @@ build_frame_blocks(const util::counted<bootproto::mem_entry> &kmap)
         size_t b = blk.count / 64;
         size_t r = blk.count % 64;
         g_alloc.memset(blk.bitmap, b*8, 0xff);
-        blk.bitmap[b] = (1 << r) - 1;
+        blk.bitmap[b] = (1ull << r) - 1;
 
         bitmap += bitmap_size(blk.count);
     }
diff --git a/src/kernel/device_manager.cpp b/src/kernel/device_manager.cpp
index ede9f99..930b20f 100644
--- a/src/kernel/device_manager.cpp
+++ b/src/kernel/device_manager.cpp
@@ -385,7 +385,7 @@ device_manager::dispatch_irq(unsigned irq)
     if (!binding.target || binding.target == ignore_event)
         return binding.target == ignore_event;
 
-    binding.target->signal(1 << binding.signal);
+    binding.target->signal(1ull << binding.signal);
     return true;
 }
 
diff --git a/src/kernel/frame_allocator.cpp b/src/kernel/frame_allocator.cpp
index b0822be..9226ac2 100644
--- a/src/kernel/frame_allocator.cpp
+++ b/src/kernel/frame_allocator.cpp
@@ -101,9 +101,9 @@ frame_allocator::free(uintptr_t address, size_t count)
         unsigned o3 = frame & 0x3f;
 
         while (count--) {
-            block.map1 |= (1 << o1);
-            block.map2[o1] |= (1 << o2);
-            block.bitmap[o2] |= (1 << o3);
+            block.map1 |= (1ull << o1);
+            block.map2[o1] |= (1ull << o2);
+            block.bitmap[o2] |= (1ull << o3);
             if (++o3 == 64) {
                 o3 = 0;
                 if (++o2 == 64) {
@@ -139,12 +139,12 @@ frame_allocator::used(uintptr_t address, size_t count)
         unsigned o3 = frame & 0x3f;
 
         while (count--) {
-            block.bitmap[o2] &= ~(1 << o3);
+            block.bitmap[o2] &= ~(1ull << o3);
             if (!block.bitmap[o2]) {
-                block.map2[o1] &= ~(1 << o2);
+                block.map2[o1] &= ~(1ull << o2);
 
                 if (!block.map2[o1]) {
-                    block.map1 &= ~(1 << o1);
+                    block.map1 &= ~(1ull << o1);
                 }
             }
 
diff --git a/src/kernel/heap_allocator.cpp b/src/kernel/heap_allocator.cpp
index ea62536..5622135 100644
--- a/src/kernel/heap_allocator.cpp
+++ b/src/kernel/heap_allocator.cpp
@@ -27,7 +27,7 @@ struct heap_allocator::free_header
 
     inline free_header * buddy() const {
         return reinterpret_cast<free_header *>(
-            reinterpret_cast<uintptr_t>(this) ^ (1 << order));
+            reinterpret_cast<uintptr_t>(this) ^ (1ull << order));
     }
 
     inline bool eldest() const { return this < buddy(); }
@@ -67,7 +67,7 @@ heap_allocator::allocate(size_t length)
 
     util::scoped_lock lock {m_lock};
 
-    m_allocated_size += (1 << order);
+    m_allocated_size += (1ull << order);
 
     free_header *block = pop_free(order);
     if (!block && !split_off(order, block)) {
@@ -95,7 +95,8 @@ heap_allocator::free(void *p)
     kassert(info, "Attempt to free pointer not known to the heap");
     if (!info) return;
 
-    m_allocated_size -= (1 << info->order);
+    size_t size = (1ull << info->order);
+    m_allocated_size -= size;
 
     block->clear(info->order);
     block = merge_block(block);
@@ -118,7 +119,7 @@ heap_allocator::reallocate(void *p, size_t old_length, size_t new_length)
     if (!info)
         return nullptr;
 
-    if (new_length <= (1 << info->order))
+    if (new_length <= (1ull << info->order))
         return p;
 
     lock.release();
@@ -180,12 +181,12 @@ heap_allocator::new_block(unsigned order)
     unsigned current = address_order(m_end);
     while (current < order) {
         register_free_block(reinterpret_cast<free_header*>(m_end), current);
-        m_end += 1 << current;
+        m_end += 1ull << current;
         current = address_order(m_end);
     }
 
     void *block = reinterpret_cast<void*>(m_end);
-    m_end += 1 << order;
+    m_end += 1ull << order;
     m_map[map_key(block)].order = order;
     return block;
 }
diff --git a/src/libraries/util/util/map.h b/src/libraries/util/util/map.h
index 09f3bc5..fd1c23b 100644
--- a/src/libraries/util/util/map.h
+++ b/src/libraries/util/util/map.h
@@ -84,7 +84,7 @@ public:
         m_nodes(nullptr)
     {
         if (capacity)
-            set_capacity(1 << log2(capacity));
+            set_capacity(1ull << log2(capacity));
     }
 
     virtual ~base_map() {
diff --git a/src/libraries/util/util/node_map.h b/src/libraries/util/util/node_map.h
index be06197..68d867f 100644
--- a/src/libraries/util/util/node_map.h
+++ b/src/libraries/util/util/node_map.h
@@ -50,7 +50,7 @@ public:
         m_nodes {nullptr}
     {
         if (capacity) {
-            m_capacity = 1 << log2(capacity);
+            m_capacity = 1ull << log2(capacity);
             m_nodes = reinterpret_cast<node_type*>(
                     alloc::allocate(m_capacity * sizeof(node_type)));
             for (size_t i = 0; i < m_capacity; ++i)
diff --git a/src/libraries/util/util/vector.h b/src/libraries/util/util/vector.h
index ed76f4f..c177c17 100644
--- a/src/libraries/util/util/vector.h
+++ b/src/libraries/util/util/vector.h
@@ -265,7 +265,7 @@ public:
     void ensure_capacity(count_t size)
     {
         if (capacity() >= size) return;
-        count_t capacity = (1 << log2(size));
+        count_t capacity = (1ull << log2(size));
         if (capacity < min_capacity)
             capacity = min_capacity;
         set_capacity(capacity);