Binary to Decimal Converter: Powers of 2 Method

To convert an unsigned binary number to decimal, add the place values of its 1 bits. The rightmost position is worth 1, the next is worth 2, then 4, 8, and so on. The worked examples below show the method for one byte and for shorter numbers.

Powers of two you need

For an 8-bit byte, positions from right (bit 0) to left (bit 7):

Bit position	Power	Value
0 (rightmost)	2⁰	1
1	2¹	2
2	2²	4
3	2³	8
4	2⁴	16
5	2⁵	32
6	2⁶	64
7 (leftmost)	2⁷	128

An eight-bit byte uses the place values 1, 2, 4, 8, 16, 32, 64, and 128. Wider integers continue with 256, 512, 1024, and further powers of two. Keep the order visible while you practise.

Method: sum the hot bits

Write the bitstring. Align it under the power headers if that helps.
Ignore every 0.
For each 1, write the power of two for that position.
Add those values. That sum is the unsigned decimal.

This is unsigned interpretation. If the value is meant as signed two's complement, you need an extra step after you know the unsigned magnitude of the pattern.

Worked example: 10110100

Bit by bit

1 0 1 1 0 1 0 0

128 + 0 + 32 + 16 + 0 + 4 + 0 + 0

128 + 32 + 16 + 4 = 180

Check with the binary converter: paste 10110100, read the decimal field.

Worked example: 00001111

Low nibble all ones: 8 + 4 + 2 + 1

Result: 15

Same idea: 2⁴ − 1 = 15 when four consecutive low bits are set.

Quick conversion table (0-16)

Decimal	Binary (4-5 bits)	Hex
0	0	0
1	1	1
2	10	2
3	11	3
4	100	4
5	101	5
7	111	7
8	1000	8
10	1010	A
15	1111	F
16	10000	10

Leading zeros

00000101 and 101 are the same unsigned value: 5. Padding only fixes the width. It does not change the sum of powers.

Protocols and CPU registers care about width. Human scratch work can drop leading zeros until you need a fixed field size again.

Bytes in text vs bare numbers

If the binary is ASCII text, each 8-bit group is a character code, not one big integer.01001000 as a number is 72. As text it is the letter H. Same bits, different job.

Use binary to text for messages. Use the binary converter when you want a single numeric value. The ASCII table bridges both views.

Doubling method (optional shortcut)

Read left to right. Start at 0. For each bit: double the running total, then add the bit.

1011 → 11

start 0

bit 1 → 0×2+1 = 1

bit 0 → 1×2+0 = 2

bit 1 → 2×2+1 = 5

bit 1 → 5×2+1 = 11

Same answer as 8+0+2+1. Pick whichever feels faster. Powers-of-two addition is usually clearer while you learn.

Practice problems

11001000
00100001
11111111
10000000 as unsigned, then as signed 8-bit

Answers

128+64+8 = 200
32+1 = 33 (ASCII '!')
255
Unsigned 128; signed 8-bit = −128

FAQ

Which bit is 2⁰?

The rightmost bit in the usual written form. If someone numbers bits from the left, check their diagram. Hardware docs sometimes number bit 0 as LSB, which matches this article.

How do I convert decimal back to binary?

Repeated divide-by-2, collecting remainders, or subtract the largest power of two that fits. The converter on this site does both directions; see also the decimal-to-binary blog post if you want a full walkthrough.

What about fractional binary?

Bits after a binary point are 1/2, 1/4, 1/8, …. Floats use a different packed layout (IEEE 754). For that, open the IEEE 754 tool.

Can I convert long bitstrings by hand?

You can, but errors creep in. Split into bytes, convert each byte, then combine with place values (×256, ×65536, …), or just paste into the converter.

Convert with the tool

Practice the four problems above on paper, then confirm in the binary converter. The full BinaryTranslator suite also shows hex and octal in the same pass if you want cross-checks.

When the bits are a message instead of a number, switch to binary to text. Same digits, different meaning.