مبدل مبنای عددی: دودویی، هشت‌هشتی، ده‌دهی و شانزده‌شانزدهی
این مبدل یک عدد صحیح را از یک مبنا به مبنای دیگر می‌برد — دودویی، هشت‌هشتی، ده‌دهی، شانزده‌شانزدهی یا هر مبنایی از ۲ تا ۳۶. محاسبه با ارزش مکانی و تقسیم‌های پیاپی را نشان می‌دهد و با تبدیل دوباره پاسخ را بررسی می‌کند.
نتیجه
مقادیر را وارد کنید و برای دیدن نتیجه «محاسبه» را بزنید.
فرمول
Each digit is multiplied by the base raised to the power of its position, starting at 0 on the right.
To convert from decimal, divide by the new base again and again; the remainders, read from last to first, are the digits.
نحوه استفاده از این ماشین‌حساب
- Type the number. For hexadecimal, use the letters A–F (upper or lower case).
- Choose the base it is written in and the base you want.
- Press Calculate to see the converted number, its decimal value and the working.
مثال‌های حل‌شده
255 in binary
Divide by 2 repeatedly: every remainder is 1, eight times.
Reading the remainders from bottom to top gives 11111111.
Binary 1011 to decimal
1 × 8 + 0 × 4 + 1 × 2 + 1 × 1 = 11.
255 in hexadecimal
255 ÷ 16 = 15 remainder 15, and 15 ÷ 16 = 0 remainder 15.
15 is the digit F, so 255 = FF.
Hexadecimal 1A3 to binary
1A3 = 1 × 256 + 10 × 16 + 3 = 419.
419 in binary is 110100011.
اشتباه‌های رایج
- Reading the remainders from top to bottom; the first remainder is the last (rightmost) digit.
- Starting the place values at 1 instead of 0: the rightmost digit is multiplied by b⁰ = 1.
- Using digits that do not exist in the base, such as 2 in binary or G in hexadecimal.
پرسش‌های متداول
How do you convert decimal to binary?
Divide by 2 and write down the remainder; repeat with the quotient until it is 0. Read the remainders from the last to the first. 13 → 1101.
How do you convert binary to decimal?
Multiply each digit by its place value (1, 2, 4, 8, … from the right) and add: 1011 = 8 + 0 + 2 + 1 = 11.
What are the letters in hexadecimal?
Hexadecimal needs 16 digits, so A–F stand for 10–15. FF = 15 × 16 + 15 = 255.