Normalisation

Y13 Lesson

Transcript

1. NORMALISATION Binary Fractions
2. 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
3. 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
4. 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?