q show division and multiplication operationthese

Question

Q. Show Division and multiplication operation?

These operations can be represented as

x + y = (N_x  × 2^Ex-Ey + N_y) × 2^Ey

and x-y = (N_x × 2^Ex-Ey-N_y) × 2^Ey

Here assumption is that exponent of x (Ex) is greater than exponent of y (Ey), Nx and Ny stand for significand of x and y correspondingly.

While for division and multiplication operations significand is required to multiplied or divided correspondingly but exponents are to be added or to be subtracted correspondingly. If we are using bias of 128 or any other bias for exponents then on addition of exponents since both exponents have bias then bias gets doubled. So we should subtract the bias from exponent on addition of exponents. But bias has to be added if we are subtracting exponents. Division and multiplication operation can be represented as:

x × y = (N_x × N_y) × 2^Ex+Ey

x ÷ y = (N_x  ÷ N_y)  × 2^Ex-Ey