arithmatic circuitII - MULTIPLIER - Consider two unsigned...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
MULTIPLIER - Consider two unsigned numbers X and Y that are of M and N bits . - i =M-1 X = X i 2 i i = 0 j =N-1 Y = Y j 2 j j = 0 Z = XY = X ·· Y × Z k 2 k k0 = MN1 + == X i 2 i i0 = M1 ⎝⎠ ⎜⎟ ⎛⎞ Y j 2 j j0 = N1 = X i Y j 2 ij + = = =
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Binary Multiplication 1 0 1 0 0 0 0 0 × 0 + Partial Products AND operation
Background image of page 2
Array Multiplier MxN Multiplication viewed as forming N Partial products of M bits each, Each row in the partial product array is either a copy of the multiplicand or a row of zeroes. then summing the appropriately shifted products to produce result P. Generation of N Partial products require NxM two bit AND gates. Binary multiplication is equivalent to a logical AND operation. Most of the area devoted to the adding of the N Partial products, which require N-1 M bit adders.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
The Array Multiplier HA FA X 0 X 1 X 2 X 3 Y 1 X 0 X 1 X 2 X 3 Y 2 X 0 X 1 X 2 X 3 Y 3 Z 1 Z 2 Z 3 Z 4 Z 5 Z 6 Z 0 Z 7
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
2’s compliment array Multiplication M-2 N-2 P = (-y M-1 2 M-1 + y j 2 j ) (-x N-1 2 N-1 + x i 2 i ) j = 0 I = 0 N-2 M-2 = ∑∑ x i y j 2 i+j + x N-1 y M-1 2 M+N-2 i=0 j=0 N-2 M-2 -( x i y M-1 2 i+M-1 + x N-1 y j 2 j+N-1 ) i=0 j=0 Two of the partial products have negative weight and thus should be subtracted .
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Y5 Y4 Y3 Y2 Y1 Y0 X5 X4 X3 X2 X1 X0 X0Y4 X0Y3 X0Y2 X0Y1 X0Y0 X1Y4 X1Y3 X1Y2 X1Y1 X1Y0 X2Y4 X2Y3 X2Y2 X2Y1 X2Y0 X3Y4 X3Y3 X3Y2 X3Y1 X3Y0 X4Y4 X4Y3 X4Y2 X4Y1 X4Y0 X5Y5 1 1 X4Y5 X3Y5 X2Y5 X1Y5 X0Y5 1 1 1 1 1 1 1 1 X5Y4 X5Y3 X5Y2 X5Y1 X5Y0 1 1 1 1 1 1 Subtraction done by taking 2’s compliment of the terms
Background image of page 8
Y5 Y4 Y3 Y2 Y1 Y0 X5 X4 X3 X2 X1 X0 1 X5Y0 X0Y4 X0Y3 X0Y2 X0Y1 X0Y0 X5Y1 X1Y4 X1Y3 X1Y2 X1Y1 X1Y0 X5Y2 X2Y4 X2Y3 X2Y2 X2Y1 X2Y0 X5Y3 X3Y4 X3Y3 X3Y2 X3Y1 X3Y0 X5Y4 X4Y4 X4Y3 X4Y2 X4Y1 X4Y0 1 X5Y5 X4Y5 X3Y5 X2Y5 X1Y5 X0Y5 P11 P10 P0
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
The MxN Array Multiplier — Critical Path HA FA FA HA HA FA FA FA FA FA FA HA Critical Path 1 Critical Path 2 Critical Path 1 & 2 All critical paths have same length speeding up one by a faster adder does not make sense .
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 31

arithmatic circuitII - MULTIPLIER - Consider two unsigned...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online