binarytodecimalhex

Binary, decimal, and hexadecimal are numeral systems used in computing. Binary is base-2, using digits 0 and 1; decimal is base-10, using digits 0 through 9; hexadecimal is base-16, using digits 0–9 and letters A–F. Converting among these bases is a common task in programming, digital design, and debugging.

Binary to decimal is done by summing the products of each bit with its power of two. For example, 1101_2 equals 1×2^3 + 1×2^2 + 0×2^1 + 1×2^0 = 8 + 4 + 0 + 1 = 13.

Binary to hexadecimal can be done by grouping bits in fours from the right. Each group converts to a single hex digit. For instance, 1011 0101_2 equals B5_16 (since 1011 is B and 0101 is 5).

Decimal to binary uses repeated division by 2, collecting remainders. For 13, the result is 1101_2. Decimal to hexadecimal uses repeated division by 16; for 255, the result is FF_16.

Hexadecimal to binary is obtained by translating each hex digit to a four-bit binary sequence. FF_16 becomes 1111 1111_2. Hexadecimal to decimal is evaluated as a base-16 value: FF_16 equals 15×16 + 15 = 255.

Notes: leading zeros are sometimes added for alignment, but do not change value. In computing, binary and hex representations are often used for low-level data, while signed numbers may require awareness of bit width and representations such as two’s complement.