How to Read Binary Numbers

Binary is just another way to write numbers. This tutorial walks through place values for eight bits, three full examples, hands-on practice, and a quick bridge to hexadecimal—no calculators required beyond addition.

Understanding binary

Our everyday decimal system is base ten: each column is a power of ten (ones, tens, hundreds, …). Binary is base two: each column is a power of two (1, 2, 4, 8, …). Digits are only 0 or 1. A 1 means “include this power of two in the sum”; a 0 means “skip it.”

When eight bits are grouped as one byte, the leftmost bit is the largest weight (128) and the rightmost is 1. Add the weights where the bit is 1 and you get the decimal value. That value often maps to a character in ASCII—see our ASCII table once you are comfortable with the sums.

Bit positions (one byte)

Read from left (most significant) to right (least significant). These are the eight weights for a single ASCII byte:

Position 7 6 5 4 3 2 1 0
Value 128 64 32 16 8 4 2 1

Worked examples

  • 01001000

    Bits on at positions 6 and 3: 64 + 8 = 72. Decimal 72 is the letter H in ASCII.

  • 01100001

    Bits on at 6, 5, and 0: 64 + 32 + 1 = 97. That is lowercase a.

  • 11111111

    Every weight is included: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. This is the largest value in an unsigned 8-bit byte (and outside standard 7-bit ASCII, which stops at 127).

Practice exercises

Cover the answers, work each sum on paper, then open the details to check.

  1. 00110011
    Show answer

    51 — the digit 3 in ASCII (codes 48–57 are the digits 0–9).

  2. 01000010
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    66 — uppercase B.

  3. 00100000
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    32 — the space character.

  4. 01111110
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    126 — the tilde ~ (last printable ASCII in the basic set).

  5. 01010101
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    85 — uppercase U (64 + 16 + 4 + 1).

From binary to hex shortcut

A full byte splits into two groups of four bits. Each group (called a nibble) maps to exactly one hexadecimal digit 0–9 or A–F. For example, 0100 is 4 in decimal, written as hex 4; 1000 is 8, hex 8, so 01001000 becomes 0x48—the same 72 / H from the first worked example.

That is why developers often memorize hex pairs for bytes: it is a compact view of the same bits you would spell out as eight zeros and ones. Our number base converter lets you check binary, decimal, and hex side by side.

Frequently asked questions

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