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# Exponent Shift Count Logic

IP.com Disclosure Number: IPCOM000101055D
Original Publication Date: 1990-Jun-01
Included in the Prior Art Database: 2005-Mar-16
Document File: 2 page(s) / 64K

IBM

## Related People

Cocanougher, D: AUTHOR [+3]

## Abstract

The shift count is a binary number, without bias, ranging from 0 to 167. The shift count provides shifting information to the B-operand shifter for final alignment with the (A+C) operand. The shift count is generated by the following formula: = (EXP A + EXP C) - EXP B - bias + 59 in which EXP A, EXP C, and EXP B are each an IEEE binary number plus its bias (i.e., EXP A = exp a + bias). The constant 59 allows the use of a unidirectional B alignment shifter.

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This is the abbreviated version, containing approximately 57% of the total text.

Exponent Shift Count Logic

The shift count is a binary number, without bias, ranging
from 0 to 167.  The shift count provides shifting information to the
B-operand shifter for final alignment with the (A+C) operand.  The
shift count is generated by the following formula:
= (EXP A + EXP C) - EXP B - bias + 59 in which
EXP A, EXP C, and EXP B are each an IEEE binary number plus its
bias (i.e., EXP A = exp a + bias).  The constant 59 allows the use
of a unidirectional B alignment shifter.

The above formula is the basis of the Multiply/Add design as
incorporated within the exponent subunit.  The figure illustrates the
hardware necessary for generating the shift count.  The A, C and
inverted B operands are initially added together by the first stage
3:2 Carry Save ADDER (CSA).  The following formula illustrates the
first stage:
= Sum + Carry of (EXP A + EXP C + (-EXP B))
= Sum + Carry of (exp a + bias + exp c + bias -
exp b - bias)       = Sum + Carry of (exp a + exp c +
(-exp b) + bias)

The second state provides the following two functions: Add the
sum and the carry from the previous stage, and add the (59 - bias).
The following formula illustrates the second stage:
= Sum + Carry of (exp a + exp c + (-exp b) + bias
+ 59 - bias)       = Sum + Carry of (exp a + exp c +
(-exp b) + 59)

The third stage uses a 2:1 full adder which adds the sum and
the carry from the previous 3:2 CSA, thus providing... 