Arithmetic for Computers October 31, 2008 Arithmetic for Computers - - PowerPoint PPT Presentation

▶

Dec 15, 2023 124 likes •209 views

Arithmetic for Computers October 31, 2008 Arithmetic for Computers ALU Arithmetic Logic Unit Performs most processor operations Control signal predicates addition subtraction logic operations shifting (w / or w / o sign extension) Figure:

SLIDE 1

Arithmetic for Computers

October 31, 2008

Arithmetic for Computers

SLIDE 2

ALU

Arithmetic Logic Unit Performs most processor operations Control signal predicates

addition subtraction logic operations shifting (w/ or w/o sign extension) Figure: ALU symbol

Arithmetic for Computers

SLIDE 3

Multiplication

Product of n with m bits = n + m bits long More complicated than addition

use addition with shifting shift left 1 bit to align with previous sum

Arithmetic for Computers

SLIDE 4

Multiplication

Product of n with m bits = n + m bits long More complicated than addition

use addition with shifting shift left 1 bit to align with previous sum Figure: Hardware for multiplication

64-bit multiplicand reg.: ∵ will be moved 32 times

32-bit multiplicand in right half; left half: 0‘s

Product: initialized to 0‘s

Arithmetic for Computers

SLIDE 5

Multiplication Algorithm

Figure: Multiplication using the simple hardware

Arithmetic for Computers

SLIDE 6

Improvement

Problem: need 64-bit adder Half bits in multiplicand are 0 Improvement:

Don’t shift the multiplicand

Shift product right!

Add it to product on the left Shift product to right Figure: Improved hardware

Arithmetic for Computers

SLIDE 7

New Algorithm

Arithmetic for Computers

SLIDE 8

Another Improvement

Save on space:

Put multiplier in product saves on speed: only single shift needed Figure: Improved hardware for multiplication

Arithmetic for Computers