Decimal to Binary Converter

The most reliable method is "Division by 2". Take your decimal number and divide it by 2. Write down the remainder (which will always be 0 or 1). Take the result (quotient) and divide by 2 again. Repeat this until you reach 0. The binary number is the sequence of remainders read from the last one you calculated (bottom) to the first (top).

The binary representation of 255 is 11111111. It is the maximum value that can be stored in an 8-bit byte, making it a significant number in computer science (often seen in IP addresses and color codes).

Computers run on electricity. It is much easier and more reliable to measure two distinct states (High Voltage = 1, Low Voltage = 0) than to measure ten subtle voltage levels to represent 0-9. This binary "On/Off" logic is the physical foundation of all modern processor architecture.

To convert back, you use "Powers of 2". Read the binary digits from right to left. The first bit is worth 1, the second is 2, the third is 4, then 8, 16, 32, and so on. Simply add up the values of all the positions where the bit is "1". For example, 101 = 4 + 0 + 1 = 5.

A "Bit" (Binary Digit) is the smallest unit of data, a single 0 or 1. A "Byte" is a group of 8 bits. While a bit can only represent 2 values, a byte can represent 256 distinct values (2^8), which is enough to store a single ASCII character like "A" or "!"

Computers use a system called "Two's Complement". The left-most bit is reserved as the "Sort Bit". If it is 1, the number is negative. To convert a negative number, you take the positive binary version, flip all the bits (0 becomes 1, 1 becomes 0), and then add 1 to the result.

Yes. Just as we have a decimal point, binary has a "radix point". Bits to the right of this point represent fractions: 1/2, 1/4, 1/8, etc. In modern computing, the IEEE 754 standard ("Floating Point") is used to store these complex fractional values efficiently.

The "Least Significant Bit" (LSB) is the right-most bit, representing the smallest value (1). The "Most Significant Bit" (MSB) is the left-most bit, representing the largest power of 2 in that number (e.g., 128 in an 8-bit number). Changing the MSB has the biggest impact on the value.

Binary strings are very long and hard for humans to read (e.g., 101101011101). Hexadecimal (Base-16) perfectly compresses every 4 bits of binary into 1 hex digit. This makes code shorter and easier to debug. For conversion, you just group binary digits into sets of 4.

A bitwise shift moves all bits to the left or right. Shifting left (<<) effectively multiplies the number by 2. Shifting right (>>) effectively divides the number by 2 (dropping the remainder). This operation is incredibly fast for processors to perform compared to standard multiplication.

If you add 1 to the maximum value (e.g., 11111111 + 1 in 8-bit), the mathematical result is 256 (100000000), but an 8-bit system only has room for the lower 8 zeroes. The result wraps around to 0. This "Integer Overflow" can cause serious bugs in software, often crashing games or financial systems.

A 32-bit integer system can store 2^32 distinct values, which is 4,294,967,296. If unsigned, the range is 0 to ~4.29 billion. If signed, it is split roughly from -2.14 billion to +2.14 billion.

No. Octal (Base-8) was popular in the early days of computing. Some experimental computers have even tried Ternary (Base-3) logic. However, binary remains the undisputed standard because of its seamless mapping to the On/Off physical switches (transistors) of hardware.

ASCII is a standard that maps binary numbers to human characters. For example, the binary number 01000001 (Decimal 65) is assigned to the uppercase letter "A". This allows computers to store text documents as long strings of binary numbers.

An IPv4 address (like 192.168.1.1) is actually four 8-bit binary numbers separated by dots. Computers see it as one continuous 32-bit string (11000000101010000000000100000001). Subnet masks use binary logic to filter network traffic.