Base conversion.md

Conversion of numbers from one base to decimal

• To convert from any system to decimal, multiply the number in the place by the weights $r^0, r^1, r^2,...$ for the left side of the decimal point and $r^{-1}, r^{-2},....$ for the right side of the decimal point where r is the base of the number system
• to convert from decimal to any other system, separate integral and fractional part. Integral part is repeatedly divided by the base untill qutient is 0 and the remainders are taken in reverse order. The Fractional part is repeatedly multiplied by the base and the integral part (before the decimal point) is taken in the same order.

Conversion from binary to other system

• To convert to octal, take 3 bits and replace them with the value of the 3 bits
• To convert to hexadecimal, take 4 bits and replace them with the value of the 4 bits.
• From octal to binary - take each value and convert it into the 3 bit representative.
• Hexa to binary - take each value and convert it into the 4 bit binary representative