Number System Converter

Step 1 — Identify the symbols

Input (Binary): Each position is either 0 or 1.

Output (Hexadecimal): Digits 0–9 plus letters A–F for values ten through fifteen.

Hex conversions use this letter-to-number map:

Step 2 — The Two-Step Method (via Decimal)

Part A — Into decimal

Number positions from the right, starting at 0. At each position, multiply that digit by 2 raised to the position index, then add every term. The total is your decimal number.

Digits after the dot: use negative powers of 2 (2⁻¹, 2⁻², …). Each place is still (digit × weight); add the fractional side to the whole side.

Part B — Out of decimal

Repeated division by 16: each remainder is one hex digit; values 10– 15 become A–F. Read remainders from last step to first.

Fractional decimal values: convert the whole part with repeated division, then multiply the fractional part by the target base over and over; each integer you get is the next digit after the radix point (same idea the calculator shows in Formulas).

Step 3 — Worked examples

Two practice values in Binary, converted to Hexadecimal using the same rules as Step 2. Example 3 uses a fractional part (digits after the radix point); the hub and pair calculators accept a single . on binary, octal, decimal, and hex inputs.

Binary "1010"
= 1×2³ + 0×2² + 1×2¹ + 0×2⁰
= 8 + 2
= 10  (decimal)

Whole part — repeated division:
10 ÷ 16 = 0  R 10 (A)

Read remainders bottom → top → A

→ tool: 0xa

Binary "1111"
= 1×2³ + 1×2² + 1×2¹ + 1×2⁰
= 8 + 4 + 2 + 1
= 15  (decimal)

Whole part — repeated division:
15 ÷ 16 = 0  R 15 (F)

Read remainders bottom → top → F

→ tool: 0xf

Binary "1010.101"
Left of . : 1×2³ + 0×2² + 1×2¹ + 0×2⁰ = 10
Right of .: 1×2^-1 + 0×2^-2 + 1×2^-3 = 0.5 + 0.125
= 10.625  (decimal)

Whole part — repeated division:
10 ÷ 16 = 0  R 10 (A)

Read remainders bottom → top → A

Fractional part — multiply by 16, integer of each product = next digit after .
  0.625×16 = 10  →  A
Digits after . (in order): .A

→ tool: 0xa.a