M.Tech. VLSI Design & CAD:Hardware Algorithms for Computer Arithmetic

First Semester I

Physics of Semiconductor Devices
IC Fabrication Technology
Digital VLSI Design
CAD Systems Environment
Research Methodology


Second Semester

Analog IC Design
Hardware Description Languages
Embedded Systems


Third Semester

Seminar
Thesis starts

Fourth Semester

Thesis


Hardware Algorithms for Computer Arithmetic

Numbers and Arithematic: Number systems, their encoding and basic arithmetic operations, Class of Fixed-Radix Number Systems, Unconventional fixed-point number systems, Representing Signed Numbers, Negative-radix number Systems, Redundant Number Systems, Residue Number Systems.

Algorithms for fast addition: Basic Addition and Counting, Bit-serial and ripple-carry adders, Addition of a constant: counters, Manchester carry chains and adders, Carry-Lookahead Adders, Carry determination as prefix computation, Alternative parallel prefix networks, VLSI implementation aspects, Variations in Fast Adders, Simple carry-skip and Carry-select adders, Hybrid adder designs, Optimizations in fast adders, Multi-Operand Addition, Wallace and Dadda trees, Parallel counters, Generalized parallel counters, Adding multiple signed numbers

High-speed multiplication: Basic Multiplication Schemes, Shift/add multiplication algorithms, Programmed multiplication, Basic hardware multipliers, Multiplication of signed numbers, Multiplication by constants, Preview of fast multipliers, High-Radix Multipliers, Modified Booth's recoding, Tree and Array Multipliers, Variations in Multipliers, VLSI layout considerations

Fast division and division through multiplication: Basic Division Schemes, Shift/subtract division algorithms, Programmed division, Restoring hardware dividers, Non-restoring and signed division, Division by constants, Preview of fast dividers, High-Radix Dividers, Variations in Dividers, Combined multiply/divide units, Division by Convergence, Hardware implementation.

Real Arithmetic: Representing the Real Numbers, Floating-point arithmetic, The ANSI/IEEE floating-point standard, Exceptions and other features, Floating-point arithmetic operations, Rounding schemes, Logarithmic number systems, Floating-point adders, Barrel-shifter design, Leading-zeros/ones counting, Floating-point multipliers, Floating-point dividers, Arithmetic Errors and Error Control.

Function Evaluation: Square-Rooting Methods, The CORDIC Algorithms, Computing logarithms, Exponentiation, Approximating functions, Merged arithmetic, Arithmetic by Table Lookup, Tradeoffs in cost, speed, and accuracy.

Implementation Topics: High-Throughput Arithmetic, Low-Power Arithmetic, Fault-Tolerant Arithmetic, Emerging Trends, Impact of Hardware Technology.