Here is the detailed explanation of Division Algorithms:
Division algorithms are methods used to perform division operations in computer arithmetic that enable computers to divide one number (the dividend) by another (the divisor) to obtain a quotient and a remainder.
• Binary division is much simpler than decimal division because here the quotient digits are either 0 or 1 and there is no need to estimate how many times the dividend or partial remainder fits into the divisor.
The division process is described in Figure:
• The devisor is compared with the five most significant bits of the dividend. Since the 5-bit number is smaller than B, we again repeat the same process.
• Now the 6-bit number is greater than B, so we place a 1 for the quotient bit in the sixth position above the dividend. Now we shift the divisor once to the right and subtract it from the dividend.
• The difference is known as a partial remainder because the division could have stopped here to obtain a quotient of 1 and a remainder equal to the partial remainder.
• Comparing a partial remainder with the divisor continues the process. If the partial remainder is greater than or equal to the divisor, the quotient bit is equal to 1 .
• The divisor is then shifted right and subtracted from the partial remainder. If the partial remainder is smaller than the divisor, the quotient bit is 0 and no subtraction is needed.
• The divisor is shifted once to the right in any case. Obviously the result gives both a quotient and a remainder.
Hardware Implementation for Signed-Magnitude Data:
• In hardware implementation for signed-magnitude data in a digital computer, it is convenient to change the process slightly.
• Instead of shifting the divisor to the right, two dividends, or partial remainders, are shifted to the left, thus leaving the two numbers in the required relative position.
• Subtraction is achieved by adding A to the 2’s complement of B. End carry gives the information about the relative magnitudes.
• The hardware required is identical to that of multiplication. Register EAQ is now shifted to the left with 0 inserted into Qn and the previous value of E is lost.
•The example is given in Figure 4.10 to clear the proposed division process.
• The divisor is stored in the B register and the double-length dividend is stored in registers A and Q.
• The dividend is shifted to the left and the divisor is subtracted by adding its 2’s complement value. E
Flowchart of Divide Operation:
Floating Point Division:
