# Scalar-Vector Multiplication

Scalar-Vector multiplication is a very important arithmetic operation in implementing signal or image processing algorithms. In this tutorial, we will discuss the hardware for multiplication between a 6X3 Matrix (A) and a 3X1 Matrix (B) and the result is a 6X1 column vector (C). This multiplication is shown below in Figure 1.

This multiplication can be achieved in two ways, either by vector-vector multiplication or by scalar-vector multiplication. In scalar-vector based multiplication, one column of matrix and one element of column vector B is fed to the computing processor. This multiplication result is accumulated with the multiplication of 2nd column of A and second element of B. Thus the matrix and vector multiplication is achieved through scalar-vector multiplication and accumulation. The multiplication between A and B can be expressed as

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The computing unit is designed using a basic Multiply and ACumulate (MAC) unit. This unit multiplies two elements and accumulate. The schematic of this MAC unit is shown below in Figure 2.