How do I convert decimal to binary?

Divide the decimal number by 2 repeatedly, recording the remainder each time. Read the remainders from bottom to top to get the binary number. Example: 42 = 101010 in binary.

What is hexadecimal used for in programming?

Hexadecimal is used for memory addresses, colour codes (#RRGGBB in web), error codes, and as a compact representation of binary data. Two hex digits represent one byte, making it more readable than raw binary.

How do I convert binary to hexadecimal?

Group binary digits into sets of 4 from right to left. Convert each group to its hex equivalent. Example: 10111110 groups as 1011 and 1110, which converts to B and E, giving BE in hexadecimal.

Binary, Decimal, Hex, and Octal: Number System Conversion Guide

Why Number Systems Matter

Computers think in binary (base 2). Humans think in decimal (base 10). Programmers use hexadecimal (base 16) as a shorthand for binary. Older systems used octal (base 8). Understanding conversions between them is fundamental to computer science, networking, and programming.

The Four Number Systems

System

Base

Digits Used

Prefix

|---|---|---|---|

Binary	2	0, 1	0b (e.g. 0b1101)
Octal	8	0-7	0o (e.g. 0o17)
Decimal	10	0-9	None
Hexadecimal	16	0-9, A-F	0x (e.g. 0xFF)

In hexadecimal: A=10, B=11, C=12, D=13, E=14, F=15

Decimal to Binary Conversion

Divide the number by 2 repeatedly, recording remainders. Read remainders bottom to top.

Example: Convert 42 to binary:

42 ÷ 2 = 21 remainder 0

21 ÷ 2 = 10 remainder 1

10 ÷ 2 = 5 remainder 0

5 ÷ 2 = 2 remainder 1

2 ÷ 2 = 1 remainder 0

1 ÷ 2 = 0 remainder 1

Reading remainders bottom to top: 101010

42 in decimal = 101010 in binary

Verification: 1×32 + 0×16 + 1×8 + 0×4 + 1×2 + 0×1 = 32+8+2 = 42 ✓

Binary to Decimal Conversion

Multiply each bit by its positional value (powers of 2) and sum.

Example: Convert 11001 to decimal:

Position values (right to left): 1, 2, 4, 8, 16

1×16 + 1×8 + 0×4 + 0×2 + 1×1 = 16+8+1 = 25

Decimal to Hexadecimal

Divide by 16 repeatedly.

Example: Convert 255 to hexadecimal:

255 ÷ 16 = 15 remainder 15 (F)

15 ÷ 16 = 0 remainder 15 (F)

Reading bottom to top: FF

255 decimal = FF hexadecimal

Common hex values to memorise:

255 = FF (maximum value of one byte)
256 = 100
16 = 10
0 = 00

Hexadecimal to Decimal

Multiply each digit by its positional value (powers of 16) and sum.

Example: Convert 2A to decimal:

2×16 + 10×1 = 32+10 = 42

Example: Convert FF to decimal:

15×16 + 15×1 = 240+15 = 255

Binary to Hexadecimal (The Shortcut)

Group binary digits in sets of 4 from right. Convert each group to its hex equivalent.

Example: Convert 10111110 to hexadecimal:

Group: 1011 | 1110

1011 = 11 = B

1110 = 14 = E

10111110 binary = BE hexadecimal

Hex-to-binary reverse: Expand each hex digit to 4 binary digits.

Why Hexadecimal Is Used in Programming

Hex is compact shorthand for binary. One hex digit represents exactly 4 binary bits. Two hex digits represent one byte (8 bits). This makes memory addresses, colour codes, and error codes readable.

Web colours: #FF5733 means R=FF(255), G=57(87), B=33(51) in decimal.

Memory: 0xFFFFFFFF is the 32-bit maximum address.

ASCII: Character 'A' is 65 decimal = 41 hex = 01000001 binary.

Using Lazyblink Binary Translator

lazyblink.com/tools/developer/binary-translator converts between all four number systems instantly. Paste any number, select the source base, and see all four conversions simultaneously. Useful for programming, networking tasks, and computer science students.