diff --git a/src/brevitas/core/quant/float.py b/src/brevitas/core/quant/float.py
index fcbed7b66..55d048936 100644
--- a/src/brevitas/core/quant/float.py
+++ b/src/brevitas/core/quant/float.py
@@ -39,6 +39,8 @@ def __init__(
             torch.tensor(float(exponent_bit_width), device=device, dtype=dtype))
         self.mantissa_bit_width = StatelessBuffer(
             (torch.tensor(float(mantissa_bit_width), device=device, dtype=dtype)))
+        if exponent_bias is None:
+            exponent_bias = 2 ** (exponent_bit_width - 1) - 1
         self.exponent_bias = StatelessBuffer(
             torch.tensor(float(exponent_bias), device=device, dtype=dtype))
         self.fp_max_val = StatelessBuffer(
diff --git a/tests/brevitas/core/test_float_quant.py b/tests/brevitas/core/test_float_quant.py
new file mode 100644
index 000000000..9997ebbda
--- /dev/null
+++ b/tests/brevitas/core/test_float_quant.py
@@ -0,0 +1,58 @@
+# Copyright (C) 2023, Advanced Micro Devices, Inc. All rights reserved.
+# SPDX-License-Identifier: BSD-3-Clause
+
+from hypothesis import given
+import mock
+import pytest
+import torch
+
+from brevitas.core.function_wrapper import RoundSte
+from brevitas.core.quant.float import FloatQuant
+from brevitas.core.scaling import ConstScaling
+from tests.brevitas.core.bit_width_fixture import *  # noqa
+from tests.brevitas.core.int_quant_fixture import *  # noqa
+from tests.brevitas.core.shared_quant_fixture import *  # noqa
+from tests.brevitas.hyp_helper import float_tensor_random_shape_st
+from tests.brevitas.hyp_helper import random_minifloat_format
+from tests.brevitas.hyp_helper import scalar_float_p_tensor_st
+from tests.marker import jit_disabled_for_mock
+
+
+@given(minifloat_format=random_minifloat_format())
+def test_float_quant_defaults(minifloat_format):
+    bit_width, exponent_bit_width, mantissa_bit_width, signed = minifloat_format
+    # specifically don't set exponent bias to see if default works
+    expected_exponent_bias = 2 ** (exponent_bit_width - 1) - 1
+    float_quant = FloatQuant(
+        bit_width=bit_width,
+        signed=signed,
+        exponent_bit_width=exponent_bit_width,
+        mantissa_bit_width=mantissa_bit_width)
+    assert expected_exponent_bias == float_quant.exponent_bias()
+    assert isinstance(float_quant.float_to_int_impl, RoundSte)
+    assert isinstance(float_quant.float_scaling_impl, ConstScaling)
+    assert isinstance(float_quant.scaling_impl, ConstScaling)
+
+
+@given(minifloat_format=random_minifloat_format())
+def test_minifloat(minifloat_format):
+    bit_width, exponent_bit_width, mantissa_bit_width, signed = minifloat_format
+    assert bit_width == exponent_bit_width + mantissa_bit_width + int(signed)
+
+
+@given(inp=float_tensor_random_shape_st(), minifloat_format=random_minifloat_format())
+@jit_disabled_for_mock()
+def test_int_quant_to_in(inp, minifloat_format):
+    bit_width, exponent_bit_width, mantissa_bit_width, signed = minifloat_format
+    exponent_bias = 2 ** (exponent_bit_width - 1) - 1
+    float_quant = FloatQuant(
+        bit_width=bit_width,
+        signed=signed,
+        exponent_bit_width=exponent_bit_width,
+        mantissa_bit_width=mantissa_bit_width,
+        exponent_bias=exponent_bias)
+    expected_out, _, _, bit_width_out = float_quant(inp)
+
+    out_quant, scale = float_quant.quantize(inp)
+    assert bit_width_out == bit_width
+    assert torch.equal(expected_out, out_quant * scale)
diff --git a/tests/brevitas/hyp_helper.py b/tests/brevitas/hyp_helper.py
index ed6f1ea87..9905d2f03 100644
--- a/tests/brevitas/hyp_helper.py
+++ b/tests/brevitas/hyp_helper.py
@@ -13,6 +13,8 @@
 import torch
 
 from tests.brevitas.common import FP32_BIT_WIDTH
+from tests.brevitas.common import MAX_INT_BIT_WIDTH
+from tests.brevitas.common import MIN_INT_BIT_WIDTH
 from tests.conftest import SEED
 
 # Remove Hypothesis check for slow tests and function scoped fixtures.
@@ -218,3 +220,21 @@ def min_max_tensor_random_shape_st(draw, min_dims=1, max_dims=4, max_size=3, wid
     min_tensor = torch.tensor(min_list).view(*shape)
     max_tensor = torch.tensor(max_list).view(*shape)
     return min_tensor, max_tensor
+
+
+@st.composite
+def random_minifloat_format(draw, min_bit_width=MIN_INT_BIT_WIDTH, max_bit_with=MAX_INT_BIT_WIDTH):
+    """"
+    Generate a minifloat format. Returns bit_width, exponent, mantissa, and signed.
+    """
+    bit_width = draw(st.integers(min_value=min_bit_width, max_value=max_bit_with))
+    exponent_bit_width = draw(st.integers(min_value=0, max_value=bit_width))
+    signed = draw(st.booleans())
+    # if no budget is left, return
+    if bit_width == exponent_bit_width:
+        return bit_width, exponent_bit_width, 0, False
+    elif bit_width == (exponent_bit_width + int(signed)):
+        return bit_width, exponent_bit_width, 0, signed
+    mantissa_bit_width = bit_width - exponent_bit_width - int(signed)
+
+    return bit_width, exponent_bit_width, mantissa_bit_width, signed