ASCII Code Table (7 bit) UNICODE (16 bit) - UTF-8 provides a 16 bit superset of ASCII.

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Presentation transcript:

ASCII Code Table (7 bit) UNICODE (16 bit) - UTF-8 provides a 16 bit superset of ASCII

2’s Complement Sign Extention Positive numbers Negative numbers

2’s Complement Arithmetic Addition Subtraction Multiplication, Division ?

Round off Errors Errors due to inherent imprecision of computers / computation

Overflow Adding two numbers which results In a sum that is too large to store: A + B A - B

Underflow A calculation in floating point that results in an intermediate result that is essentially zero.

Floating Point Numbers Example: x Sign Fraction Exponent

Single Precision Floating Point Numbers IEEE Standard Single Precision Floating Point Numbers are 32 bits long: S EEEEEEEE FFFFFFFFFFFFFFFFFFFFFFF Sign – 1 bit Exponent – 8 bits Fraction – 23 bits The value V: If E=255 and F is nonzero, then V= NaN ("Not a number") If E=255 and F is zero and S is 1, then V= - Infinity If E=255 and F is zero and S is 0, then V= Infinity If 0<E<255 then V= (-1)**S * 2 ** (E-127) * (1.F) If E=0 and F is nonzero, then V= (-1)**S * 2 ** (-126) * (0.F) ("unnormalized" values”) If E=0 and F is zero and S is 1, then V= - 0 If E=0 and F is zero and S is 0, then V = 0

Double Precision Floating Point Numbers IEEE Standard Double Precision Floating Point Numbers are 64 bits long: S EEEEEEEEEEE FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF Sign – 1 bit Exponent – 11 bits Fraction – 52 bits The value V: If E=2047 and F is nonzero, then V= NaN ("Not a number") If E=2047 and F is zero and S is 1, then V= - Infinity If E=2047 and F is zero and S is 0, then V= Infinity If 0<E<2047 then V= (-1)**S * 2 ** (E-1023) * (1.F) If E=0 and F is nonzero, then V= (-1)**S * 2 ** (-1022) * (0.F) ("unnormalized" values) If E=0 and F is zero and S is 1, then V= - 0 If E=0 and F is zero and S is 0, then V= 0

Chapter 3 Digital Logic Structures The Transistor CMOS Devices Implementing Logic with CMOS Devices Combinational Logic Circuits Decoders Mux’s Full Adder PLA’s

Introduction to MOS N-type MOS

N-Type MOS Devices

P-Type MOS Devices

CMOS Device - Inverter p channel device n channel device CMOS Inverter 3-5 volts

CMOS NOR Gate NOR Gate

CMOS OR Gate OR Gate

CMOS AND Gate AND Gate

2 BIT Decoder