Design Con 2015
Breaking News
Comments
Newest First | Oldest First | Threaded View
<<   <   Page 3 / 3
KarlS01
User Rank
Manager
How computers used to do binary multiply and divide
KarlS01   12/7/2013 11:11:18 AM
NO RATINGS
Hi, Tom:  As you said, multiply is a series of additions -- but not dependent on the magnitude of the multiplier, only the number of 1 bits after making both operands positive by complementing if negative.

It is a shift and add sequence starting with the low order bit of the multiplier if it is a 1 add the multiplicand to the double wide product high order and shift right 1 into low order. if multiplier bit is zero, just shift product right one.

Repeat until higher multiplier bits are zero or shifts equal to multipl;ier width. If the high bits are all 0s, then just shift for the remaining word width.

Division was trial subtraction by subtracting the divisore fron the dividend, if the result was positive shift 1 into the quotient high bit else shift 0.  Remainder is left in the reg that held the high order dividend and the quotient in the low order.

If the signs of the dividend and divisor were different, complement at the end.

This is best I remember, maybe a few details missing. The shifts amounted to *2 and /2 and the add/subtract would wind up in the appropriate power of two positions.

I think the constant used in the compiler is 1/10 so they are multiplying by the reciprical of 10 to effectively divide by 10.

krisi
User Rank
CEO
Re: math links
krisi   12/7/2013 10:01:00 AM
NO RATINGS
Pretty cool math...I wonder whether they teach something like that in vlsi classes...Kris

Brian_D
User Rank
Freelancer
math links
Brian_D   12/6/2013 7:56:58 PM
NO RATINGS
There's some nice material about constant division on the companion website for "Hacker's Delight":

http://www.hackersdelight.org/divcMore.pdf

Also, VHDL has a nifty fixed point math package:

http://www.eda.org/fphdl/

-Brian

sa_penguin
User Rank
Manager
Goldschmidt?
sa_penguin   12/6/2013 7:40:07 PM
NO RATINGS
Sounds a bit like Goldschmidt division: converting the factor 1/10 into X/(2^n). Multiply by X, shift N bits, done. Taking the upper 16 bits of a 32-bit word is equal to a 16-bit shift.

I suspect 1/10 doesn't translate perfectly to binary so, just like 1/3 becomes 0.33... you get a hex factor of 0x1999... in your division.

<<   <   Page 3 / 3


Most Recent Comments
Top Comments of the Week
Flash Poll
Like Us on Facebook

Datasheets.com Parts Search

185 million searchable parts
(please enter a part number or hit search to begin)
EE Life
Frankenstein's Fix, Teardowns, Sideshows, Design Contests, Reader Content & More
<b><a href=Betajet">

The Circle – The Future's Imperfect in the Present Tense
Betajet
5 comments
The Circle, a satirical, dystopian novel published in 2013 by San Francisco-based writer Dave Eggers, is about a large, very powerful technology company that combines aspects of Google, ...

Max Maxfield

Recommended Reads From the Engineer's Bookshelf
Max Maxfield
27 comments
I'm not sure if I read more than most folks or not, but I do I know that I spend quite a lot of time reading. I hate to be idle, so I always have a book or two somewhere about my person -- ...

Martin Rowe

Make This Engineering Museum a Reality
Martin Rowe
Post a comment
Vincent Valentine is a man on a mission. He wants to make the first house to ever have a telephone into a telephone museum. Without help, it may not happen.

Rich Quinnell

Making the Grade in Industrial Design
Rich Quinnell
16 comments
As every developer knows, there are the paper specifications for a product design, and then there are the real requirements. The paper specs are dry, bland, and rigidly numeric, making ...

Special Video Section
The LT8640 is a 42V, 5A synchronous step-down regulator ...
The LTC2000 high-speed DAC has low noise and excellent ...
How do you protect the load and ensure output continues to ...
General-purpose DACs have applications in instrumentation, ...
Linear Technology demonstrates its latest measurement ...
10:29
Demos from Maxim Integrated at Electronica 2014 show ...
Bosch CEO Stefan Finkbeiner shows off latest combo and ...
STMicroelectronics demoed this simple gesture control ...
Keysight shows you what signals lurk in real-time at 510MHz ...
TE Connectivity's clear-plastic, full-size model car shows ...
Why culture makes Linear Tech a winner.
Recently formed Architects of Modern Power consortium ...
Specially modified Corvette C7 Stingray responds to ex Indy ...
Avago’s ACPL-K30T is the first solid-state driver qualified ...
NXP launches its line of multi-gate, multifunction, ...
Doug Bailey, VP of marketing at Power Integrations, gives a ...
See how to ease software bring-up with DesignWare IP ...
DesignWare IP Prototyping Kits enable fast software ...
This video explores the LT3086, a new member of our LDO+ ...
In today’s modern electronic systems, the need for power ...