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1. Module I 8 Hours Number Representation: Numbers and arithmetic,what is computer arithmetic?, motivating examples, numbers and their encodings, fixed-radix positional number systems, number radix conversion, classes of number representations. Representing signed numbers: signed-magnitude representation, biased representations, complement representations, two's and 1's-complement numbers, direct and indirect signed arithmetic, using signed positions or signed digits. Redundant number systems: coping with the carry problem, redundancy in computer arithmetic, digit sets and digit-set conversions, generalized signed-digit numbers. Module II 8 Hours Addition/Subtraction: Basic addition and counting, bit-serial and ripple-carry adders, conditions and exceptions, analysis of carry propagation, carry completion detection, addition of a constant, counters, manchester carry chains and adders. Carry- lookahead adders: unrolling the carry recurrence, carry- lookahead adder design, ling adder and related designs, carry determination as prefix computation, alternative parallel prefix networks, VLSI implementation aspects. Module III 8 Hours Multiplication: Shift/add multiplication algorithms, programmed multiplication, basic hardware multipliers, multiplication of signed numbers, multiplication by constants, preview of fast multipliers. High-radix multipliers: radix-4 multiplication, modified booth's recoding, using carrysave adders. Module IV 8 Hours Division: Basic Division Schemes: Shift/subtract division algorithms, programmed division, restoring hardware dividers, non-restoring and signed division, division by constants, radix-2 SRT division. High-radix dividers: Basics of high-radix division, using carry-save adders, radix-4 SRT division, Module V 8 Hours Real Arithmetic: Floating-point representations, the ANSI/IEEE floating-point standard, basic floating-point algorithms, conversions and exceptions, rounding schemes, logarithmic number systems. Floating-Point Operations: Floating-point adders/ subtractors , pre- and postshifting , rounding and exceptions, floating-point multipliers and dividers

2. Module III 8 Hours Multiplication: Shift/add multiplication algorithms, programmed multiplication, basic hardware multipliers, multiplication of signed numbers, multiplication by constants, preview of fast multipliers. High-radix multipliers: radix-4 multiplication, modified booth's recoding, using carrysave adders. Module IV 8 Hours Division: Basic Division Schemes: Shift/subtract division algorithms, programmed division, restoring hardware dividers, non-restoring and signed division, division by constants, radix-2 SRT division. High-radix dividers: Basics of high-radix division, using carry-save adders, radix-4 SRT division, Module V 8 Hours Real Arithmetic: Floating-point representations, the ANSI/IEEE floating-point standard, basic floating-point algorithms, conversions and exceptions, rounding schemes, logarithmic number systems. Floating-Point Operations: Floating-point adders/ subtractors , pre- and postshifting , rounding and exceptions, floating-point multipliers and dividers