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 32 X 32 Bit Multiplication Using Urdhva Triyakbhyam (Vertically and crosswise) for two Binary numbers

 

Consider two 32 bit numbers A and B respectively as follows, where each number has 23 bit floating point part; 8 bit integer part and 1 bit sign bit.

A= a31 a30a29a28a27a26a25a24a23 a22a21a20a19a18a17a16a15a14a13a12a11a10a9a8 a7a6a5a4a3a2a1a0

(X2) (X1) (X0)

B= b31 b30b29b28b27b26b25b24b23 b22b21b20b19b18b17b16b15b14b13b12b11b10b9b8b7b6b5b4b3b2b1b0

(Y2) (Y1) (Y0)

 

 

 

Thus the above multiplication process can be viewed as

X2 X1 X0

* Y2 Y1 Y0

--------------------------

SABC

Where, CP= C= X0Y0

CP= B= X1Y0+X0Y1

CP= A= X1Y1

S=X2 (xor) Y2

 

 BLOCK DIAGRAM

 

 

Figure 4.5

A block diagram representing 8-bit multiplication