Question

2. Given the block diagram for the signed 2's complement multiplier below. show the contents of registers A and B for each clock cycle when the multiplicand -3/8 and the multiplier = -3/4. Verify your answer. Product A (accumulator) Multiplier 4-BIT FULL ADDER Cin l's COMPLEMENTER Multiplicand

Answer 1

Answer:

There are 3 main methods for multiplying binary numbers in 2's complement representation: shift-and-add method, Booth/Wallace method, and array method.

Booth's algorithm:

This is a kind of algorithm that uses a more straightforward approach. This algorithm also has the benefit of speeding up the multiplication process and it is very efficient too. Binary multiplication which has a signed number uses this type of algorithms named Booth's algorithm.

Booth’s algorithm for two complements multiplication:

Sterot Count-n M - Multiplicand Q = Multiplier 10 ol Po, LA-A-MT 60 TA-A+M Arthemetic Shift right count -count - I Count to?

1. Multiplier and multiplicand are placed in the Q and M register respectively.
2. The result for this will be stored in the AC and Q registers.
3. Initially, AC and Q_-1 register will be 0.
4. Multiplication of a number is done in a cycle.

1. A 1-bit register Q_-1 is placed right of the least significant bit Q₀ of the register Q.
2. In each of the cycle, Q₀ and Q_-1 bits will be checked.
   1. If Q₀ and Q_-1 are 11 or 00 then the bits of AC, Q and Q_-1 are shifted to the right by 1 bit. (ii) If the value is shown 01 then multiplicand is added to AC. After addition, AC, Q₀, Q_-1 register are shifted to the right by 1 bit. (iii) If the value is shown 10 then multiplicand is subtracted from AC. After subtraction AC, Q₀, Q_-1 register is shifted to the right by 1 bit.

Basically, Booth’s algorithm uses the concept of an arithmetic right shift in which the leftmost bit is not only shifted right by 1 bit but it also remains in the original position.

As given in a condition of multiplicand = -3/8 and the multiplier = -3/4,

at this it is simple that the weighted sum of 2's complement is represented by the "-" sign, then as in above the multiplicand NxN that is -3x8 and the multiplier is -3x4. So, generally, the product will be between the

multiplicand (-8)₁₀ and multiplier (-4)₁₀, then the product is

M = -8 = 1000

Q = -4 = 1100

we well get a product