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Binary to Decimal & Hexadecimal Converter
Bi-directional converter between Binary (Base 2), Decimal (Base 10), Hexadecimal (Base 16), and Octal (Base 8). Features an interactive bit register, two’s complement signed math, and power-of-2 breakdown steps.
CMaintained by Computer Systems Desk
Published Last verified
Allowed: 0-9
Quick Samples:
Interactive 8-Bit Register
Click bits to toggleConversion Results
Awaiting inputEnter a binary, decimal, hex, or octal value above to view multi-base conversions
Results, statistical ratios, and detailed amortization ledgers will appear here once values are provided.
CMaintained by Computer Systems Desk
Published Last verified
Calculation Methodology & Formula
Binary expansion multiplies each bit position by increasing powers of two: N = \sum (b_i \times 2^i). Fractional bits expand through negative powers of two (2^{-1} = 0.5, 2^{-2} = 0.25).
N_{10} = \sum_{i=0}^{n} (b_i \times 2^i) + \sum_{j=1}^{m} (f_j \times 2^{-j})Worked Example: 8-Bit Binary Expansion
Convert binary 11010110 to decimal and hexadecimal.
input:11010110
from Base:Base 2 (Binary)
Expected Output214 (Decimal) | 0xD6 (Hexadecimal)
128 + 64 + 0 + 16 + 0 + 4 + 2 + 0 = 214. 214 ÷ 16 = 13 (D) R 6 => 0xD6.
Technical Constraints & Limitations
- Standard integers convert up to JavaScript safe integer limits (2^53 - 1, or 9,007,199,254,740,991).
- Two’s complement representations are modeled specifically for signed 8-bit (-128 to 127), 16-bit, and 32-bit registers.
Frequently Asked Questions
How do you convert binary to decimal manually?
List each bit from right to left starting at position 0. Multiply each bit by 2 raised to its position power (1, 2, 4, 8, 16, 32, 64, 128...), then sum all positive products.
What is Two’s Complement?
Two’s complement is the standard binary encoding used by computer microprocessors to represent signed negative integers. The most significant bit (MSB) acts as the sign flag, with 1 indicating a negative value.
Why do computer systems use hexadecimal?
Hexadecimal is base 16, where exactly one hex digit represents 4 binary bits (one nibble). An 8-bit byte is represented cleanly by exactly two hex digits (e.g., 11111111 = FF), making it compact and human-readable.