chapter4 - CSCI-365 Computer Organization Lecture Chapter 4...

Info iconThis preview shows pages 1–21. Sign up to view the full content.

View Full Document Right Arrow Icon
CSCI-365 Computer Organization Lecture Note : Some slides and/or pictures in the following are adapted from: Computer Organization and Design, Patterson & Hennessy, ©2005 Some slides and/or pictures in the following are adapted from: slides ©2008 UCB Chapter 4
Background image of page 1

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

View Full DocumentRight Arrow Icon
Truth Tables Uniquely Define CL Function
Background image of page 2
Truth Table A truth table defines the outputs of a logic block for each set of inputs E.g., Consider a block with 3 inputs A, B, C and an output E that is true only if exactly 2 inputs are true (DONE IN CLASS)
Background image of page 3

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

View Full DocumentRight Arrow Icon
Logic Gates
Background image of page 4
Logic Gates
Background image of page 5

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

View Full DocumentRight Arrow Icon
2-input gates extend to n-inputs N-input XOR is the only one which isn’t so obvious It’s simple: XOR is a 1 iff the # of 1s at its input is odd
Background image of page 6
Boolean Algebra George Boole, 19 th Century mathematician Developed a mathematical system (algebra) involving logic later known as “Boolean Algebra” Primitive functions: AND, OR and NOT The power of BA is there’s a one-to-one correspondence between circuits made up of AND, OR and NOT gates and equations in BA + means OR,• means AND, x means NOT
Background image of page 7

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

View Full DocumentRight Arrow Icon
Canonical Forms Sum of products
Background image of page 8
Laws of Boolean Algebra
Background image of page 9

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

View Full DocumentRight Arrow Icon
BA: Circuit & Algebraic Simplification BA also great for circuit verification Circ X = Circ Y? use BA to prove!
Background image of page 10
Canonical Forms
Background image of page 11

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

View Full DocumentRight Arrow Icon
Truth Table Gates (e.g., majority circ.) (DONE IN CLASS)
Background image of page 12
Common Logic Blocks - Multiplexor Multiplexor or selector: one of N inputs is reflected on the output depending on the value of the log 2 N selector bits. E.g., 2-input mux
Background image of page 13

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

View Full DocumentRight Arrow Icon
Takes in N inputs and activates one of 2 N outputs I 0 I 1 O 0 O 1 O 2 O 3 0 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 1 2-to-4 Decoder I 0 O 0 Common Logic Blocks - Decoder I 1 O 1 O 2 O 3 2-4 Decoder (DONE IN CLASS)
Background image of page 14
Arithmetic and Logic Unit Most processors contain a special logic block called “Arithmetic and Logic Unit” (ALU)
Background image of page 15

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

View Full DocumentRight Arrow Icon
Arithmetic and Logic Unit A common way to implement the ALU is to provide a CL block for each of the possible ALU functions The inputs, A and B, get distributed to all the blocks The output of the proper block is selected with a mux Every function of the ALU is computed internally to the ALU on every cycle, but only one of the results is sent to the output
Background image of page 16
Arithmetic and Logic Unit The logical operations as defined by the MIPS ISA are bitwise operations – In the case of AND, the resultant bit r i is generated as a i AND b i . The circuit to perform this operation is simply a collection of 32 AND gates Similarly, the OR block is a collection of 32 OR gates The add/subtract block is significantly more complex
Background image of page 17

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

View Full DocumentRight Arrow Icon
Adder/Subtracter Design -- how? Truth-table, then determine canonical form, then minimize and implement as we’ve seen before This technique is only effective for very narrow adders, truth table too large for wider adders Look at breaking the problem down into smaller pieces that we can cascade or hierarchically layer We will design the smaller pieces individually, then wire them together to create entire wide adder
Background image of page 18
1-Bit Adder (DONE IN CLASS)
Background image of page 19

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

View Full DocumentRight Arrow Icon
Multiplexor selects between ADD, OR, AND operations 1-Bit ALU with ADD, OR, AND
Background image of page 20
Image of page 21
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/26/2009 for the course MATH AND C CSCI365 taught by Professor Laurencetianruoyang during the Spring '09 term at St. Francis Xavier, Antigonish.

Page1 / 76

chapter4 - CSCI-365 Computer Organization Lecture Chapter 4...

This preview shows document pages 1 - 21. Sign up to view the full document.

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