Reference chart

Binary, decimal and hex table

Binary counts in twos, decimal in tens and hexadecimal in sixteens. This table gives 0 to 15 in all three, the powers of two you'll meet in electronics, the byte values that come up again and again, and how to convert four bits at a time.

0 to 15

Hex uses 0–9, then A to F for 10 to 15. One hex digit is exactly four bits. The last column is the Gray code for the same number, where each step changes only one bit.

Decimal	Binary	Hex	Gray code
0	0000	0	0000
1	0001	1	0001
2	0010	2	0011
3	0011	3	0010
4	0100	4	0110
5	0101	5	0111
6	0110	6	0101
7	0111	7	0100
8	1000	8	1100
9	1001	9	1101
10	1010	A	1111
11	1011	B	1110
12	1100	C	1010
13	1101	D	1011
14	1110	E	1001
15	1111	F	1000

Powers of two

Each binary place is worth double the one before. These are the place values, and the number of patterns that many bits can make.

Power	Decimal	Hex	Where you'll meet it
2⁰	1	0x1	The lowest bit
2¹	2	0x2	Patterns in one bit: 0 or 1
2²	4	0x4	Patterns in two bits
2³	8	0x8	Patterns in three bits
2⁴	16	0x10	Patterns in four bits
2⁵	32	0x20	Patterns in five bits
2⁶	64	0x40	Patterns in six bits
2⁷	128	0x80	The top bit of a byte
2⁸	256	0x100	Patterns in a byte
2¹⁰	1024	0x400	A 10-bit ADC, like an Arduino Uno's
2¹²	4096	0x1000	A 12-bit ADC
2¹⁶	65,536	0x10000	Patterns in 16 bits
2²⁴	16,777,216	0x1000000	Colours with 8 bits each of red, green and blue
2³²	4,294,967,296	0x100000000	Patterns in 32 bits

How far n bits count

n bits count from 0 to 2ⁿ − 1. A signed number gives up the top bit to say whether it's negative.

Bits	Counts to	In hex	Signed range
4	15	0xF	−8 to 7
8	255	0xFF	−128 to 127
10	1023	0x3FF	−512 to 511
16	65,535	0xFFFF	−32,768 to 32,767
32	4,294,967,295	0xFFFFFFFF	−2,147,483,648 to 2,147,483,647

An Arduino Uno's int is 16 bits, so it tops out at 32,767; a long is 32 bits.

Common bytes

Hex	Binary	Decimal	What it is
0x00	0000 0000	0	Every bit off
0x01	0000 0001	1	Only the lowest bit
0x0F	0000 1111	15	Low nibble: a mask that keeps the right four bits
0xF0	1111 0000	240	High nibble: a mask that keeps the left four bits
0x55	0101 0101	85	Alternate bits, a test pattern
0xAA	1010 1010	170	The other alternating pattern
0x7F	0111 1111	127	The biggest signed byte
0x80	1000 0000	128	Only the top bit; −128 as a signed byte
0xFF	1111 1111	255	Every bit on; −1 as a signed byte

Converting four bits at a time

Four bits make one hex digit, a nibble, so you never need to convert a long number in one go.

Hex to binary: write each digit as four bits. 0x3C is 3 and C, 0011 1100.
Binary to hex: group the bits in fours from the right, pad the left group with zeros, and swap each group for its digit. 1011010 is 0101 1010, 0x5A.
Hex to decimal: multiply each digit by its place, 1, 16, 256 and so on. 0xC8 is 12 × 16 + 8 = 200.
Decimal to hex: divide by 16. The answer is the left digit and the remainder the right: 200 ÷ 16 = 12 remainder 8, so C8.

In Arduino and C code, write hex as 0x3C and binary as 0b00111100. Both are the number 60.

Free lesson

Now build it yourself

Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.

Try it yourself: free lesson

“One or zero” is lesson 1 of 6 in Gate Grove, Digital Logic World 1. Free with an account. It’s open as soon as you sign up.

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Work it out

Binary, decimal and hex converterDecimal, binary and hex, with every bit's place value added up.

The ideas behind it

Questions people ask

How do you convert binary to hex?

Split the bits into groups of four from the right, padding the left group with zeros, and swap each group for its hex digit. 1011010 becomes 0101 1010, which is 5 and A: 0x5A, or 90.

What is 0xFF in decimal?

255. FF is 15 × 16 + 15, and in binary it's 1111 1111: all eight bits of a byte on. It's the biggest number one byte can hold.

Why do programmers use hex instead of binary?

Each hex digit is exactly four bits, so a byte is always two hex digits. 0xB4 is far easier to read and type than 1011 0100, and you can still see the bits by converting each digit on its own.

What is a nibble?

Four bits: half a byte. One nibble is one hex digit, from 0 (0000) to F (1111). A byte has a high nibble, the left four bits, and a low nibble, the right four.