Decimal to Hexadecimal Conversion — Step by Step Guide

Introduction

Hexadecimal (base 16) is one of the most widely used number systems in programming. Whether you are working with CSS colour codes, memory addresses, or debugging binary data, you need to convert decimal to hex frequently. This guide teaches the standard division-by-16 method with clear worked examples.

🔧 Try it now: Decimal to Hex Converter — instant conversion with step-by-step division shown.

The Division-Remainder Method

To convert any decimal number to hexadecimal:

1. Divide the decimal number by 16
2. Record the remainder (0–15, where 10=A, 11=B, 12=C, 13=D, 14=E, 15=F)
3. Use the quotient as the new number
4. Repeat until the quotient becomes 0
5. Read remainders from bottom to top — that is your hex result

Hex Digit Reference

Decimal	Hex	Decimal	Hex
0	0	8	8
1	1	9	9
2	2	10	A
3	3	11	B
4	4	12	C
5	5	13	D
6	6	14	E
7	7	15	F

Worked Examples

Example 1: Convert 255 to Hex

Step	Division	Quotient	Remainder	Hex Digit
1	255 ÷ 16	15	15	F
2	15 ÷ 16	0	15	F

Read bottom to top: FF

Verification: F×16 + F×1 = 15×16 + 15 = 240 + 15 = 255 ✓

Example 2: Convert 4096 to Hex

Step	Division	Quotient	Remainder	Hex Digit
1	4096 ÷ 16	256	0	0
2	256 ÷ 16	16	0	0
3	16 ÷ 16	1	0	0
4	1 ÷ 16	0	1	1

Read bottom to top: 1000

This makes sense — 4096 = 16³, so it is exactly “1” followed by three zeros in hex.

Example 3: Convert 500 to Hex

Step	Division	Quotient	Remainder	Hex Digit
1	500 ÷ 16	31	4	4
2	31 ÷ 16	1	15	F
3	1 ÷ 16	0	1	1

Read bottom to top: 1F4

Comparison: Decimal, Binary, Octal, Hex

Decimal	Binary	Octal	Hex
10	1010	12	A
16	10000	20	10
100	1100100	144	64
255	11111111	377	FF
4096	1000000000000	10000	1000

Notice how hex is much more compact than binary — every hex digit represents exactly 4 binary bits.

Why Hex is Used in Programming

• CSS colors: #FF5733 = RGB(255, 87, 51)
• Memory addresses: 0x7FFFFFFF is easier to read than the binary equivalent
• Machine code: Assembly uses hex for opcode bytes
• IPv6 addresses: Written in hex groups (e.g., 2001:0db8::)
• Unicode: Code points like U+0041 = ‘A’

Common Mistakes

1. Forgetting A–F mapping — Remainders 10–15 must be written as A–F, not as two decimal digits
2. Reading remainders top-down — Always read from the last remainder to the first
3. Wrong division — Divide by 16 (not 8 or 2) for hexadecimal
4. Confusing hex 10 with decimal 10 — Hex 10 = decimal 16

Frequently Asked Questions

How do I convert decimal to hex quickly?

For numbers under 256, divide by 16 once: quotient is the first hex digit, remainder is the second. For example, 200 ÷ 16 = 12 remainder 8, so 200 = C8 hex.

What is the hex equivalent of decimal 256?

256 ÷ 16 = 16 R0, 16 ÷ 16 = 1 R0, 1 ÷ 16 = 0 R1 → 100 hex. This equals 16² which is exactly “1” followed by two zeros in hex.

Why do CSS colors use hex?

Each color channel (Red, Green, Blue) ranges 0–255, which maps perfectly to two hex digits (00–FF). This gives 6 hex characters for a full RGB color.

Can I convert hex fractions?

This guide covers whole numbers. Fractional hex conversion requires multiplying the decimal fraction by 16 repeatedly — a less common operation.

What is the 0x prefix?

0x is a programming convention indicating a hexadecimal literal. 0xFF means “FF in hex” = 255 decimal. Our converter accepts input with or without this prefix.

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