# CONVERSION - INTRODUCTION

**3/5**

Conversion from decimal to its equivalent representation in the radix r system is carried out by separating the number into its integer and fraction parts and converting each part separately. The conversion of a decimal integer into a base r representation is done by successive divisions by r and accumulation of the remainders. The conversion of a decimal fraction to radix r representation is accomplished by successive multiplications by r and accumulation of the integer digits so obtained. Figure 3-1 demonstrates these procedures.

The conversion of decimal 4L6875 into binary is done by first separating the number into its integer part 41 and fraction part .6875. The integer part is converted by dividing 41 by r = 2 to give an integer quotient of 20 and a remainder of L The quotient is again divided by 2 to give a new quotient and remainder. This process is repeated until the integer quotient becomes 0. The coefficients of the binary number are obtained from the remainders with the first remainder giving the low-order bit of the converted binary number.

The fraction part is converted by multiplying it by r = 2 to give an integer and a fraction. The new fraction (without the integer) is multiplied again by 2 to give a new integer and a new fraction. This process is repeated until the fraction part becomes zero or until the number of digits obtained gives the required accuracy. The coefficients of the binary fraction are obtained from the integer digits with the first integer computed being the digit to be placed next to the binary point. Finally, the two parts are combined to give the total required conversion.

**3/5**