NORMALISATION Binary Fractions 

Normalisation ■ Is the process of ensuring there is only one way of representing a floating point number in binary. ■ To highlight this, look at the following numbers, we already know we can’t store a decimal point from AS but we do know that during conversion we place the decimal point directly after the sign bit. ■ What are the following numbers? 0.001 0100 0.010 0011 0.100 0010 

Rule of normalisation ■ All positive numbers must start 0.1 ■ All negative numbers must start 1.0 ■ In doing so, we increase the accuracy we are able to achieve by utilising the positions after the decimal point. ■ Take the following positive number from the previous slide: 0.001 0100 ■ Move the point before the one and count the shifts ■ Minus these shifts from the original exponent, with a four bit mantissa this leaves 0.100 0010 ■ This is now the normalised version of the floating point number 2.0 

Rule of normalisation ■ All positive numbers must start 0.1 ■ All negative numbers must start 1.0 ■ Take the following negative numbers: 1.111 0100 1.110 0011 1.100 0010 1.000 0001 ■ What do they represent?