Hex Binary Decimal Engineering Reference

1. The Nibble Lookup (4-bit Base)

Memorize this. All larger Hex numbers are just sequences of these 16 patterns.

Hex	Binary	Decimal	Hex	Binary	Decimal
0x0	0000	0	0x8	1000	8
0x1	0001	1	0x9	1001	9
0x2	0010	2	0xA	1010	10
0x3	0011	3	0xB	1011	11
0x4	0100	4	0xC	1100	12
0x5	0101	5	0xD	1101	13
0x6	0110	6	0xE	1110	14
0x7	0111	7	0xF	1111	15

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2. Powers of Two (Bit Flags & Shifts)

Used for setting bits (1 << n), memory addressing, and flag definitions.

A. Low Byte (Bits 0-7)

Bit (\(n\))	Logic (1 << n)	Hex Value	Decimal	Note
0	1 << 0	0x01	1
1	1 << 1	0x02	2
2	1 << 2	0x04	4
3	1 << 3	0x08	8
4	1 << 4	0x10	16
5	1 << 5	0x20	32
6	1 << 6	0x40	64
7	1 << 7	0x80	128	MSB of a Byte (int8)

B. High Byte / Word (Bits 8-15)

Bit (\(n\))	Logic (1 << n)	Hex Value	Decimal	Note
8	1 << 8	0x100	256	Start of high byte
9	1 << 9	0x200	512
10	1 << 10	0x400	1,024	1 Kilo (KB)
11	1 << 11	0x800	2,048
12	1 << 12	0x1000	4,096	4 KB (Page Size)
13	1 << 13	0x2000	8,192
14	1 << 14	0x4000	16,384
15	1 << 15	0x8000	32,768	MSB of a Short (int16)

C. Large Boundaries (Bits 16 & 31)

Bit (\(n\))	Logic (1 << n)	Hex Value	Decimal	Note
16	1 << 16	0x0001 0000	65,536	64 KB
...	...	...	...
20	1 << 20	0x0010 0000	1,048,576	1 Mega (MB)
...	...	...	...
30	1 << 30	0x4000 0000	1,073,741,824	1 Giga (GB)
31	1 << 31	0x8000 0000	2,147,483,648	MSB of an Int (int32)

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3. Standard Type Maximums (Masks)

Commonly used for masking operations (val & 0xFF) or checking overflow.

Type	Hex Mask	Binary Visual	Decimal (Unsigned)
UINT8_MAX	0xFF	1111 1111	255
UINT16_MAX	0xFFFF	... 1111 1111	65,535
UINT32_MAX	0xFFFFFFFF	(32 ones)	4,294,967,295
INT32_MAX	0x7FFFFFFF	0111 ... 1111	2,147,483,647