Hex to Decimal – Převodník

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Understanding the Hexadecimal Number System

Hexadecimal (hex) is a base-16 number system that uses 16 distinct symbols: the digits 0–9 and the letters A–F (where A=10, B=11, C=12, D=13, E=14, F=15). Hex is widely used in computing as a human-friendly way to represent binary data, because every 4 binary digits (bits) correspond to exactly one hex digit — making hex a compact shorthand for binary.

Each position in a hex number represents a power of 16:

Hex to decimal conversion: Multiply each hex digit by its place value (power of 16) and sum the results.

Example: 2F4A₁₆ = 2×4096 + F(15)×256 + 4×16 + A(10)×1 = 8,192 + 3,840 + 64 + 10 = 10,106

Hex numbers are typically prefixed with 0x in programming (e.g., 0x2F4A), or followed by h in assembly language (e.g., 2F4Ah), to distinguish them from decimal numbers.

Decimal to Hexadecimal Conversion

Converting from decimal to hexadecimal uses the same repeated-division method as binary conversion, but dividing by 16 instead of 2.

Method: Repeatedly divide by 16, recording the remainder at each step. Remainders 10–15 are written as A–F. Read remainders from bottom to top.

Example: Convert 1,500 to hex

• 1500 ÷ 16 = 93, remainder 12 → C
• 93 ÷ 16 = 5, remainder 13 → D
• 5 ÷ 16 = 0, remainder 5 → 5

Read bottom to top: 5DC₁₆

Verify: 5×256 + D(13)×16 + C(12)×1 = 1,280 + 208 + 12 = 1,500 ✓

Example: Convert 255 to hex (the maximum value of a byte)

• 255 ÷ 16 = 15, remainder 15 → F
• 15 ÷ 16 = 0, remainder 15 → F

Result: FF₁₆ — which is why 255 is represented as 0xFF in code and #FFFFFF (white) in CSS colors uses all three channels at max (255, 255, 255).

Quick mental conversion tip: For numbers under 256, split into the highest multiple of 16 (the first hex digit) and the remainder (second hex digit). 180 = 11×16 + 4 = B4₁₆. 200 = 12×16 + 8 = C8₁₆.

Hex Color Codes: Web and Design Applications

One of the most common everyday uses of hexadecimal is CSS and web color codes. Colors are specified as #RRGGBB, where RR, GG, and BB are two-digit hex values (00–FF) for red, green, and blue channels respectively.

Each channel (00–FF) provides 256 levels × 3 channels = 16,777,216 possible colors (16.7 million). The shorthand #RGB notation (e.g., #F5A) expands each digit to two identical digits: #FF55AA — used in CSS when both hex digits in a pair are identical.

Modern CSS also supports #RRGGBBAA (8 hex digits) for colors with transparency (alpha channel), where AA defines opacity from 00 (fully transparent) to FF (fully opaque). Example: #FF573380 = the orange-red at 50% opacity (80₁₆ = 128₁₀ ≈ 50%).

Hex in Programming and Computing

Hexadecimal appears throughout programming, hardware documentation, and computer science:

Memory addresses: RAM and processor addresses are expressed in hex. A 64-bit memory address might look like 0x7FFE0B4C3A20. Hex is used because it compactly represents the underlying binary, and 2 hex digits = exactly 1 byte — making address arithmetic intuitive.

Machine code and disassembly: CPU instructions are encoded as hex bytes. The x86 instruction MOV EAX, 0x42 compiles to hex bytes B8 42 00 00 00. Security researchers and low-level programmers read hex dumps to understand or reverse-engineer software.

ASCII character encoding: ASCII maps characters to numbers 0–127. In hex: 'A' = 0x41, 'a' = 0x61, space = 0x20, '0' = 0x30. The pattern is consistent — uppercase letters start at 0x41, lowercase at 0x61 (exactly 0x20 = 32 difference, which is why XOR-ing a letter with 0x20 toggles its case).

IPv6 addresses: 128-bit IPv6 addresses are written as 8 groups of 4 hex digits: 2001:0DB8:AC10:FE01:0000:0000:0000:0001. Each group represents 16 bits (4 hex digits × 4 bits each). IPv4 addresses can also be expressed in hex: 192.168.1.1 = 0xC0A80101.

Error codes: Windows stop codes ("Blue Screen of Death") are hex: 0x0000007E, 0xC0000005. UNIX errno codes, HTTP status codes in network packets, and BIOS POST codes all use hex. Recognizing common hex patterns helps troubleshoot system issues.

Binary, Octal, Decimal, Hex: The Complete Conversion Reference

The four number systems used in computing and how they relate:

Shortcuts for fast conversion:

• Binary ↔ Hex: Group binary digits in sets of 4 (from right), convert each group to one hex digit. No division needed. 1010 1100 1111₂ = A, C, F = ACF₁₆
• Binary ↔ Octal: Group binary digits in sets of 3 (from right), convert each group. 001 010 011₂ = 1, 2, 3 = 123₈
• Hex ↔ Octal: Convert via binary as an intermediary — hex to binary (4 bits per hex digit), then binary to octal (3 bits per octal digit)

Practical Hex Calculations and Tips

A few useful techniques for working with hex in practice:

Hex addition: Add column by column, carrying when the sum reaches 16. Example: 3A + 2F:

• Units column: A(10) + F(15) = 25 decimal = 19₁₆ → write 9, carry 1
• Sixteens column: 3 + 2 + 1(carry) = 6
• Result: 69₁₆ = 105 decimal. Check: 58 + 47 = 105 ✓

Checking divisibility in hex: A hex number is divisible by 16 if the last digit is 0 (same as divisibility by 10 in decimal). It's divisible by 2 if the last hex digit is even (0,2,4,6,8,A,C,E).

Hex in URLs and encoding: URLs encode special characters using percent-encoding: a space becomes %20 (0x20 = 32 = space in ASCII). The @ symbol = %40 (0x40 = 64 = '@' in ASCII). Knowing ASCII hex codes helps decode encoded URLs.

Hash functions output hex: MD5 produces 128-bit (32 hex chars) output. SHA-256 produces 256-bit (64 hex chars) output. Example SHA-256 hash: a665a45920422f9d417e4867efdc4fb8a04a1f3fff1fa07e998e86f7f7a27ae3 — always 64 hex characters regardless of input size. This is what you see when verifying file downloads against checksums.

Frequently Asked Questions