1. Overview Fractions & Sign Extension Floating Point Representations
Binary/Hex Arithmetic
Binary Logic
Binary Gates (OR, AND, NOT, NOR, NAND)
Truth Tables
DeMorgan’s Law
Concept of Vectors & Masks

2. Understanding Sign Extension, Fractions
Binary fractions (the binary point)
Round off error

3. 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

4. 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

5. Binary Arithmetic Unsigned add & subtract
2’s complement add & subtract
Overflow

6. Binary Logic
NOT
AND OR
XOR
NAND
NOR
Truth tables
DeMorgan’s Theorem