Mastering Digital Arithmetic

Explains decimal, binary, and hexadecimal number systems, bases, LSB and MSB, and conversions with four-bit grouping for compact hex representation.

Explore unsigned number representation and how bits encode magnitude in four-bit and eight-bit ranges, including 14 as 1110 and 00001110, and why 180 and 28 don't fit four bits.

Explore sign magnitude, one complement, and two's complement representations for integers, examine the MSB as sign bit, and compare ranges and implications for arithmetic.

Explore binary arithmetic and learn sign extension to preserve signedness when extending bit width; pad unsigned numbers with zeros and signed numbers with ones to maintain value.

Explore binary addition from one-bit to n-bit operations, aligning lsb to lsb, using carries, and applying two's complement signed arithmetic with overflow rules.

Explore binary multiplication by forming partial products, aligning least significant bits, and using placeholders for unsigned and signed operations, with examples like 13×3.

Explore left and right shifts, which multiply or divide by powers of two by discarding bits, and apply shift-based tricks to multiply a four-bit number by a constant like 14.

Learn binary division by stepping through the process with bits, comparing partial remainders to the divisor, performing subtractions, and extracting the quotient and remainder.

Explain fixed point representation using qm formats and two's complement for signed and unsigned numbers. Demonstrate fixed point addition, subtraction, and multiplication, and discuss resolution, range, overflow, and underflow.

Explore floating point representation, including single and double precision, IEEE standards, sign, exponent and mantissa, normalization and denormalized forms, special values, and basic arithmetic operations.

Master the VHDL numeric_std package for arithmetic using unsigned and signed types, two's complement, and arithmetic, comparison, shift, rotate, resize, and conversion functions, with practice in Modelsim or EDA playground.

Review binary, decimal, and hexadecimal representations and base conversions. Explore unsigned number representations, binary arithmetic, and fractional formats—including fixed point and floating point—and the VHDL numeric package for arithmetic operations.