What's the fastest way to convert binary to decimal by hand?

Write the powers of two under each binary digit (starting from 1 on the right and doubling leftward), then add up the powers wherever the binary digit is 1. For 1011: the digits sit over 8, 4, 2, 1 — add 8 + 2 + 1 (skipping the 4, since that digit is 0) to get 11.

Do I read binary digits left to right or right to left?

The rightmost digit is always the smallest place value (2⁰ = 1), same as decimal's rightmost digit being the ones place. Assign powers of two starting from the right (1, 2, 4, 8, 16...) and work leftward.

How do I convert a binary number with more than 8 digits?

The same method scales to any length — just keep doubling the place values leftward (16, 32, 64, 128, 256, 512...) for each additional digit, and sum the ones where the bit is 1. It gets error-prone by hand past about 12-16 digits; that's where a converter using exact integer arithmetic is worth using instead of manual addition.

What's 11111111 in decimal?

255 — eight 1s in a row is the maximum value a single byte (8 bits) can hold, since 128+64+32+16+8+4+2+1 = 255. This is why byte values in networking, color channels, and file formats max out at 255.

Guide

How to convert binary to decimal by hand, step by step

Every binary digit is worth a power of two. Add up the ones where there's a 1, and that's the decimal value.

By Buğra SözeriPublished September 25, 2026

Binary is a positionalnumber system, exactly like decimal — the only difference is the base. In decimal, each digit’s place is worth a power of 10 (ones, tens, hundreds...); in binary, each digit’s place is worth a power of 2 (1, 2, 4, 8, 16...). Converting binary to decimal by hand is just assigning those place values and adding up the ones where the binary digit is 1.

The positional-value method

Write the binary number, and above each digit write its place value, starting from the rightmost digit at 2⁰ = 1 and doubling for each position moving left. For an 8-digit (one-byte) number, the place values are:

128	64	32	16	8	4	2	1
2⁷	2⁶	2⁵	2⁴	2³	2²	2¹	2⁰

Then sum the place values wherever the binary digit above them is 1, and skip the ones where it’s 0.

Worked example: 1011

Take 1011. Line it up against the place values 4, 2, 1... wait — for a 4-digit number the place values, right to left, are 1, 2, 4, 8:

Digit	1	0	1	1
Place value	8	4	2	1

Add up the place values wherever the digit is 1: 8 + 2 + 1 = 11 (skip the 4, since that digit is 0). So 1011 in binary equals 11 in decimal.

One-byte reference table

Binary	Decimal
00000001	1
00001010	10
00010000	16
01111111	127
10000000	128
11111111	255

255 is the largest value one byte can hold — all eight bits set to 1 sums to 128+64+32+16+8+4+2+1 = 255, which is why byte-based values throughout computing (RGB color channels, IPv4 octets, file permission masks) top out at that number.

Where hand conversion gets error-prone

The method scales to any length, but tracking eight or more place values and adding them correctly by hand gets error-prone quickly — a single missed digit throws off the whole sum. For longer binary strings, like a 32-bit network address or a hash fragment, a binary to decimal converter using exact integer arithmetic avoids both the arithmetic mistakes and the precision loss that JavaScript’s native number type introduces past 53 bits. For the reverse direction — decimal to binary — the process is repeated division by 2 instead of summed powers; see the decimal to binary converter for that direction.

Frequently asked questions

What's the fastest way to convert binary to decimal by hand?: Write the powers of two under each binary digit (starting from 1 on the right and doubling leftward), then add up the powers wherever the binary digit is 1. For 1011: the digits sit over 8, 4, 2, 1 — add 8 + 2 + 1 (skipping the 4, since that digit is 0) to get 11.
Do I read binary digits left to right or right to left?: The rightmost digit is always the smallest place value (2⁰ = 1), same as decimal's rightmost digit being the ones place. Assign powers of two starting from the right (1, 2, 4, 8, 16...) and work leftward.
How do I convert a binary number with more than 8 digits?: The same method scales to any length — just keep doubling the place values leftward (16, 32, 64, 128, 256, 512...) for each additional digit, and sum the ones where the bit is 1. It gets error-prone by hand past about 12-16 digits; that's where a converter using exact integer arithmetic is worth using instead of manual addition.
What's 11111111 in decimal?: 255 — eight 1s in a row is the maximum value a single byte (8 bits) can hold, since 128+64+32+16+8+4+2+1 = 255. This is why byte values in networking, color channels, and file formats max out at 255.

Sources & references

Authoritative references cited by this piece. Verified by Buğra Sözeri on the dates shown and re-checked at every deploy.

NIST — Positional notation (Mathematics Glossary) — NIST's reference on positional numeral systems, which underlies the powers-of-two method used here(as of 2026-09-25)
IEEE 754-2019 — Standard for Floating-Point Arithmetic — The standard governing how binary represents fractional and floating-point values in computing(as of 2026-09-25)