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An array multiplier is used to find the product of a 3-bit number with a 4-bit number. How many 4 bits addresses are required to perform multiplication?

An array multiplier is used to find the product of a 3-bit number with a 4-bit number. How many 4 bits addresses are required to perform multiplication? Correct Answer 2

Concept:

An array multiplier is a digital combinational circuit used for multiplying two binary numbers by employing an array of full adders and half adders.

  • This array is used for the nearly simultaneous addition of the various product terms involved.
  • To form the various product terms, an array of AND gates is used before the Adder array.
  • The multiplication of two binary numbers can be done with one micro-operation through a combinational circuit that forms the product bits all at once.


One example is mentioned below:

[ alt="F1 Tapesh.S 27-11-20 Savita D1" src="//storage.googleapis.com/tb-img/production/20/12/F1_Tapesh.S_27-11-20_Savita_D1.png" style="width: 194px; height: 145px;">

Assuming A = a1a0 and B = b1b0, the various bits of the final product term P can be written as:-
1. P0 = a0b0
2. P1 =a1b0 + b1a0
3. P2 = a1b1 + c1
4. P3 = c2

c1: The carry generated during the addition for the P1 term

c2: The carry generated during the addition for the P2 term

Calculation:

Given numbers are 3 bit and 4 bit.

Let A = a2a1a0 and B = b3b2b1b0

The structure is shown below

[ alt="F1 Tapesh.S 27-11-20 Savita D2" src="//storage.googleapis.com/tb-img/production/20/12/F1_Tapesh.S_27-11-20_Savita_D2.png" style="width: 315px; height: 186px;">

Conclusion:

A total of two 4 bit addresses are required for the multiplication operation.

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