Logic Design / Processor and
Control Units
Tony Diep
Topics to be discuss…
• Functional properties of digital
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•
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integrated circuits
Instruction sets
Number presentation
Register and ALU organization
Data paths
Logic Gates
• Binary information is represented in
digital computer called signals.
• Electrical signal as voltages are chosen
to represent 2 recognizable states
0.5 volt = 0, 1.5 volt = 1
Logic Gates
• Gates are logic circuits that manipulate
binary information.
• Gates are blocks of hardware that
produce signals of binary 1 or 0 when
input logic requirement are satisfied.
Logic Gates
Logic Gates
Logic Gates
• NAND gate
• NOR gate
• Exclusive OR
Combinational & Sequential
Circuits
• A CC can be described by a truth table is
having the binary relationship when the n
input variables and the m output variable.
• A SC employ signals that affect storage
elements (flip-flop) only at discrete instants
of time. Synchronization is achieved by time
device called clock pulse generator that
produces periodic train of clock pulses.
Flip - Flop
• Flip-flop is part of the electronic
component responsible for the storage
of data in memory.
• SR, JK, D flip-flops
• Difference among various flip-flops is in
the number of inputs they possess and
the manner in which inputs affect the
binary state.
Simple SR Flip-Flop
A "set/reset" flip-flop in which activating
the "S" input will switch it to one stable
state and activating the "R" input will
switch it to the other state.
JK Flip-Flop
• An edge triggered SR flip-flop with extra logic
such that only one of the R and S inputs is
enabled at any time. This prevents a race
condition which can occur when both inputs
of an RS flip-flop are active at the same time.
In a JK flip-flop the R and S inputs are
renamed J and K. The set input (J) is only
enabled when the flip-flop is reset and K
when it is set.
D Flip-Flop
• A digital logic device that stores the
status of its "D" input whenever its
clock input makes a certain transition
(low to high or high to low). The
output, "Q", shows the currently stored
value.
Instruction Set
• Vocabulary of machine language.
• Popular MIPS instruction set used Sony,
NEC, Silicon Graphic.
MIPS Instruction
• Million Instructions Per Second (MIPS)
• Operates on two source operands and
places the result in one destination
operand.
• Translation from C to MIPS assembly
language instructions is performed by
compiler.
Simples MIPS Instructions
• add a, b, c -- meaning a = b + c
• sub a, b, c -- meaning a = b - c
• C statement -- f=(g+h) – (i+j)
•
add t0, g, h
add t1, i, j
sub f, t0, t1
#temp variable t0 contains g+h
#temp variable t1 contains i+j
#f gets t0 – t1, which is
(g+h) - (i+j)
Number Representation
• Base 2 representation
• Example: 1011 base 2 in a MIPS word (32
bits) is
Unsigned and Sign
• Two’s complement -- meaning leading
0s mean positive, and leading 1s mean
negative.
• Sign bit determine a number is positive
or negative (with 0 considered positive)
Binary to Decimal Conversion
Addition and Subtraction
• Addition in binary starts from right to
left, with carries passed to the next
digit to the left.
• Subtracting can be done directly such
as 7 – 6, or via addition using the two’s
complement representation of –6.
ALU
• Arithmetic Logic Unit
• A device that performs the arithmetic
operations like addition and subtraction
or logical operation like AND and OR.
• ALU can be constructed w/ 4 hardware
building blocks (AND, OR, Inverter, and
Multiplexor).
1-Bit ALU
• 1-bit ALU for AND and OR
1-Bit Adder
1-bit adder has 3 inputs and 2 outputs.
1-Bit ALU w/ Addition
1-bit ALU that performs AND, OR, and
addition.
32-bit ALU
A 32-bit ALU
constructed
from 32 1-bit
ALUs
Building Data Path
• For every instruction, the first 2 steps
are identical:
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•
Send the Program Counter (PC) to the
memory that contains the code and fetch
the instruction from that memory
Read one or two registers, using fields of
the instruction to select the registers to
read.
Building Data Path
An abstract view of the implementation of
the MIPS subset.
PC supplies
instruction address
to the instruction
memory
Register operands
used by an
instruction are
specified by fields of
that instructions
Register operands
can be operated on
to compute a
memory address (for
load or store)
If the instruction is an
arithmetic-logical
instruction, the result from
the ALU must be written to
a register
Reference
• CS 444 Lecture Notes
• Computer Organization & Design by
David Patterson and John L Hennessy
• http://www.brunel.ac.uk/~castjjg/hndcf
und/material/logic/part5.htm