Suppose we have to add 12.5 and 1.25 using fixed point arithmetic
1) integer form Scale factor -2 and
2) fractional form Scale factor 4
Do we consider the decimal point(.) as a digit in each case?
In fixed point arithmetic, the location of the decimal point is predetermined and does not change during the calculations. Therefore, we do not consider the decimal point (.) as a digit in each case. Instead, we need to apply the appropriate scaling factor to perform the addition.
1) Integer form Scale Factor -2:
To perform the addition using integer form scale factor -2, we need to shift the values to the left by 2 digits before adding them.
12.5 * 10^(-2) = 1250
1.25 * 10^(-2) = 125
Now, we can simply add the shifted values:
1250 + 125 = 1375
Therefore, the sum of 12.5 and 1.25 using integer form scale factor -2 is 13.75.
2) Fractional form Scale Factor 4:
To perform the addition using fractional form scale factor 4, we need to shift the values to the right by 4 digits before adding them.
12.5 * 10^(4) = 125000
1.25 * 10^(4) = 12500
Now, we can add the shifted values:
125000 + 12500 = 137500
To convert the result back to normal decimal representation, we need to shift the decimal point 4 digits to the left:
13.75 * 10^(-4) = 0.001375
Therefore, the sum of 12.5 and 1.25 using fractional form scale factor 4 is 0.001375.