1. Dividison & Overflow
Given a dividend X and a divisor D, generate a quotient Q and a remainder R
X = Q  D + R (with R  D-1)
X = Q  D + R  Q  D + D – 1
X  D  ( Q + 1 ) – 1
Q  2n (largest number stored in a register)
X  D  ( 2n ) – 1
X  D  2n-1 – 1
X < D  2n-1

2. Fraction Sequential Division
Given a dividend X and a divisor D, generate a quotient Q and a remainder R
X = Q  D + R (3.10)
X/ 22n-2 = Q / 2n-1  D / 2n-1 + R / 22n-2 (I) ∵
X  largest number stored in a two-length register (22(n-1) for a register with n bits);
Q, D, R  largest number stored in a single-length register (2n-1 for a register with n bits); ∴
XF = X/ 22n-2 < 1;
QF = Q/ 2n-1 < 1; DF = D/ 2n-1 < 1; RF = R/ 2n-1 < 1;
Rewrite Equation (I) as follows
XF = QF  DF + 2–(n-1)  RF