Numbers

Here’s a complete list of numeric data types (both signed and unsigned) with their bit sizes, memory usage, and value ranges.

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🧮 1️⃣ Integer Types

Type	Signed?	Bits	Bytes	Minimum Value	Maximum Value
4-bit nibble	Unsigned	4	0.5	0	15
4-bit nibble	Signed	4	0.5	-8	+7
8-bit (byte / int8 / char)	Unsigned	8	1	0	255
8-bit (byte / int8 / char)	Signed	8	1	-128	+127
16-bit (short / int16 / smallint)	Unsigned	16	2	0	65,535
16-bit (short / int16 / smallint)	Signed	16	2	-32,768	+32,767
32-bit (int / int32 / long in C)	Unsigned	32	4	0	4,294,967,295
32-bit (int / int32)	Signed	32	4	-2,147,483,648	+2,147,483,647
64-bit (bigint / long / int64)	Unsigned	64	8	0	18,446,744,073,709,551,615 (≈1.8×10¹⁹)
64-bit (bigint / int64)	Signed	64	8	-9,223,372,036,854,775,808	+9,223,372,036,854,775,807
128-bit (int128, not standard in C/Python)	Unsigned	128	16	0	3.4×10³⁸
128-bit (int128)	Signed	128	16	-1.7×10³⁸	+1.7×10³⁸

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🔢 2️⃣ Floating-Point Types (IEEE 754 Standard)

Type	Bits	Bytes	Approx. Range	Precision (significant digits)
Half precision (float16)	16	2	±6.10×10⁴	~3 decimal digits
Single precision (float32)	32	4	±3.40×10³⁸	~7 decimal digits
Double precision (float64)	64	8	±1.80×10³⁰⁸	~15–16 decimal digits
Quad precision (float128)	128	16	±1.20×10⁴⁹³²	~33–34 decimal digits

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🧠 3️⃣ Decimal / Arbitrary Precision (in databases or languages like Python)

Type	Description	Bits	Range	Memory
Decimal(p, s)	Fixed precision decimal (e.g., in SQL)	Variable	Depends on precision p	Usually 1–17 bytes
Python int	Arbitrary precision	Unlimited	Limited by available memory	Dynamic allocation
BigDecimal (Java)	Arbitrary precision	Variable	Depends on precision	Dynamic allocation

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⚙️ 4️⃣ Other Variants

Type	Common Usage	Bits	Bytes	Range
bool / boolean	True/False values	1 (usually stored as 8 bits)	1	0 or 1
bfloat16	ML applications (reduced precision float16)	16	2	Similar range as float32 but ~2–3 digits precision
float8 (experimental)	ML accelerators (e.g., NVIDIA Hopper)	8	1	Range varies; ~1–2 digits precision

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🧩 Memory Summary

Bits	Bytes	Example Type(s)
1	0.125	bool
4	0.5	nibble
8	1	byte, uint8, int8
16	2	short, float16
32	4	int32, float32
64	8	int64, double
128	16	int128, float128

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🔢 Numeric Data Types — Ranges, Sizes, and Memory

Below is a complete reference for integer, floating-point, and special numeric types, including their bit width, memory usage, and value ranges.

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🧮 Integer Types

Type	Signed?	Bits	Bytes	Minimum Value	Maximum Value
4-bit nibble	Unsigned	4	0.5	0	15
4-bit nibble	Signed	4	0.5	−8	+7
8-bit (byte / int8)	Unsigned	8	1	0	255
8-bit (byte / int8)	Signed	8	1	−128	+127
16-bit (short / int16 / smallint)	Unsigned	16	2	0	65,535
16-bit (short / int16 / smallint)	Signed	16	2	−32,768	+32,767
32-bit (int / int32)	Unsigned	32	4	0	4,294,967,295
32-bit (int / int32)	Signed	32	4	−2,147,483,648	+2,147,483,647
64-bit (bigint / int64)	Unsigned	64	8	0	18,446,744,073,709,551,615
64-bit (bigint / int64)	Signed	64	8	−9,223,372,036,854,775,808	+9,223,372,036,854,775,807
128-bit (int128)	Unsigned	128	16	0	≈3.4×10³⁸
128-bit (int128)	Signed	128	16	≈−1.7×10³⁸	≈+1.7×10³⁸

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🌊 Floating-Point Types (IEEE 754)

Type	Bits	Bytes	Approx. Range	Precision (Significant Digits)
Half precision (float16)	16	2	±6.10×10⁴	~3 digits
Single precision (float32)	32	4	±3.40×10³⁸	~7 digits
Double precision (float64)	64	8	±1.80×10³⁰⁸	~15–16 digits
Quad precision (float128)	128	16	±1.20×10⁴⁹³²	~33–34 digits

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💰 Decimal & Arbitrary Precision Types

Type	Description	Bits	Range	Memory
Decimal(p, s)	Fixed precision decimal (used in SQL)	Variable	Depends on precision p	1–17 bytes (typical)
Python int	Arbitrary-precision integer	Dynamic	Limited by memory	Grows dynamically
Java BigDecimal	Arbitrary precision decimal	Dynamic	Depends on precision	Grows dynamically

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⚙️ Other Variants & Special Types

Type	Usage	Bits	Bytes	Range
bool / boolean	True/False	1 (bit, often stored as 1 byte)	1	0 or 1
bfloat16	ML accelerators (TPUs, GPUs)	16	2	Same range as float32, ~2–3 digits precision
float8 (experimental)	AI hardware (e.g., NVIDIA Hopper)	8	1	Range and precision vary (~1–2 digits)

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🧠 Memory Summary

Bits	Bytes	Common Type(s)
1	0.125	bool
4	0.5	nibble
8	1	byte, int8
16	2	short, float16
32	4	int32, float32
64	8	int64, double
128	16	int128, float128

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💡 Notes

• Signed vs Unsigned: Signed types reserve one bit for sign representation (two’s complement). Unsigned types use the full bit range for positive values.

• Floating-point precision: Higher bit width → more accurate representation of decimals, not necessarily a wider range.

• Arbitrary-precision numbers: Used when fixed bit-width numbers can overflow (e.g., cryptography, high-precision finance).