Step-by-Step Number System Conversion Examples
Master number system conversions with these explicit mathematical examples showing step-by-step calculations.
Decimal to Binary Conversion Example (Decimal 45 to Binary)
- Step 1: 45 / 2 = 22, Remainder 1 (Least Significant Bit)
- Step 2: 22 / 2 = 11, Remainder 0
- Step 3: 11 / 2 = 5, Remainder 1
- Step 4: 5 / 2 = 2, Remainder 1
- Step 5: 2 / 2 = 1, Remainder 0
- Step 6: 1 / 2 = 0, Remainder 1 (Most Significant Bit)
Result: Reading the remainders from bottom to top, decimal 45 is 101101 in binary.
Binary to Decimal Conversion Example (Binary 101101 to Decimal)
- Step 1: 1 × 2^5 = 32
- Step 2: 0 × 2^4 = 0
- Step 3: 1 × 2^3 = 8
- Step 4: 1 × 2^2 = 4
- Step 5: 0 × 2^1 = 0
- Step 6: 1 × 2^0 = 1
Result: Summing the values (32 + 0 + 8 + 4 + 0 + 1), binary 101101 is 45 in decimal.
Binary to Octal Conversion Example (Binary 101101 to Octal)
Group the binary digits into sets of three starting from the right (LSB):
- Group 1 (Right): 101 in binary = 5 in octal
- Group 2 (Left): 101 in binary = 5 in octal
Result: Binary 101101 is 55 in octal.
Binary to Hexadecimal Conversion Example (Binary 101101 to Hex)
Group the binary digits into sets of four starting from the right (LSB), padding with leading zeros if necessary:
- Group 1 (Right): 1101 in binary = 13 in decimal = D in Hexadecimal
- Group 2 (Left): 0010 (padded) in binary = 2 in Hexadecimal
Result: Binary 101101 is 2D in hexadecimal.
