Computer organisation anaylization (COA) question with solution

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Multiply -3 and +4 using Booth multiplication algorithm with clearly

showing the steps as well as the flow chart of the algorithm.

Q.2 Describe the functionality of the carry save multiplier.

Q.3 What are the division restoring and non-division restoring techniques?

Q.4 Write the names of the addressing modes used in the following

instructions?

(a) Y -> ADD Y 10

(b) AC<- AC + [A]

(c) R<- R + [[R1]]

In the above flowchart, initially, AC and Qn + 1 bits are set to 0, and the SC is a sequence counter that represents the total bits set n, which is equal to the number of bits in the multiplier. There are BR that represent the multiplicand bits, and QR represents the multiplier bits. After that, we encountered two bits of the multiplier as Qn and Qn + 1, where Qn represents the last bit of QR, and Qn + 1 represents the incremented bit of Qn by 1. Suppose two bits of the multiplier is equal to 10; it means that we have to subtract the multiplier from the partial product in the accumulator AC and then perform the arithmetic shift operation (ashr). If the two of the multipliers equal to 01, it means we need to perform the addition of the multiplicand to the partial product in accumulator AC and then perform the arithmetic shift operation (ashr), including Qn + 1. The arithmetic shift operation is used in Booth's algorithm to shift AC and QR bits to the right by one and remains the sign bit in AC unchanged. And the sequence counter is continuously decremented till the computational loop is repeated, equal to the number of bits (n).

The sum of two digits can never carry more than a 1, and the sum of two digits plus 1 can also never carry more than 1. For example, in decimal, {\displaystyle 9+9=18}{\displaystyle 9+9=18}, which carries a 1; {\displaystyle 9+9+1=19}{\displaystyle 9+9+1=19}, which also carries a 1. When adding three figures, we can add the first two and produce a sum and the carry digits; then add the sum and the carry digits to the third figure and produce a sum and the carry digits. In binary, the only digits are zero and one, and so {\displaystyle 0+0=0}0+0=0, {\displaystyle 0+1=1}

Restoring division is usually performed on the fixed point fractional numbers. When we perform division operations on two numbers, the division algorithm will give us two things, i.e., quotient and remainder. This algorithm is based on the assumption that 0 < D < N. With the help of digit set {0, 1}, the quotient digit q will be formed in the restoring division algorithm. The division algorithm is generally of two types, i.e., fast algorithm and slow algorithm. Goldschmidt and Newton-Raphson are the types of fast division algorithm, and STR algorithm, restoring algorithm, non-performing algorithm, and the non-restoring algorithm are the types of slow division algorithm.

Implied / Implicit Addressing Mode

Stack Addressing Mode

Immediate Addressing Mode

Direct Addressing Mode

Indirect Addressing Mode

Register Direct Addressing Mode

Register Indirect Addressing Mode

Relative Addressing Mode

Indexed Addressing Mode

Base Register Addressing Mode

Auto-Increment Addressing Mode

Auto-Decrement Addressing Mode

The definition of the instruction itself specify the operands implicitly.

The operand is contained at the top of the stack.

The booth algorithm is a multiplication algorithm that allows us to multiply the two signed binary integers in 2's complement, respectively. It is also used to speed up the performance of the multiplication process. It is very efficient too. It works on the string bits 0's in the multiplier that requires no additional bit only shift the right-most string bits and a string of 1's in a multiplier bit weight 2k to weight 2m that can be considered as