Boolean Logic

What notations are for NOT

¬x, x (“-” above the x), x ′

what is an F in NOT

T

What is a T in NOT

F

What are the notations for OR

x ∨ y, x + y

What is FF in OR

F

What is FT in OR

T

What is TF in OR

T

What is TT in OR

T

What are the notations for AND

xy, x . y, x^y

What is FF in AND

F

What is FT in AND

F

What is TF in AND

F

What is TT in AND

T

What are the notations for XOR

x ⊕ y = (x ∧ ¬y) ∨ (¬x ∧ y)

x ⊕ y = xy + xy (with lines over first y and second x)

What is FF in XOR

F

What is FT in XOR

T

What is TF in AND

T

What is TT in XOR

F

What does NOR mean

NOT OR

What are the notations for NOR

x ↓ y = ¬(x ∨ y)

Why is NOR sufficient to construct all functions?

Because NOR is functionally complete, meaning any boolean function can be expressed using only NOR gates. (AND OR NOT can be made using NOR gates)

What is FF in NOR

T

What is FT in NOR

F

What is TF in NOR

F

What is TT in NOR

F

What is NAND

NOT AND

Why is NAND sufficient to construct all functions?

NAND is functionally complete, NAND can create the basic gates (AND, OR, NOT) needed for any logical expression.

What are the notations for NAND

x ↑ y = ¬(x ∧ y)

What is FF in NAND

T

What is FT in NAND

T

What is TF in NAND

T

What is TT in NAND

F

Who is George Boole

Made Boolean Logic Algebra

Boolean Algebra

is a general model for mathematical systems

What values are computes with this BL

two values (T/F), (0/1)

What did Claude Shannon do

showed that for every boolean expression there exists a switching network through which current flows exactly when the expression is true.

George Stibitz

Made first electrical computer, and made model k (boolean logic using electromechanical relays)

What order do we do truth tables?

0011, 0101

what does a half adder do?

Add two 1 bit numbers

what does a full adder do?

Adds 3 numbers: 2 bts and one carry from previous addition.

What is Abstraction

Solid State physics

Transistor circiuits

Logic Desing

Systems design

System Software

Application Software

Theory

Who is Charles Babbage

Made Difference and Analytical Engine

Konrad Zuse

Made first programmable functional computer: z1, z2, z3

Vannevar Bush

Mechanical analog computer—differential analyzer

Howard Aiken

Harvard Mark I—electromechanical machine

J Presper Eckert and John Mauchly

– ENIAC – EDVAC – UNIVAC

Ada Lovelace

Made computer coding

Grace Hopper

Wrote Harvard Mark I manual – Developed early compiler technology – Major influence in COBOL

The ENIAC Six

Jean Jennings Bartik, Kay McNulty Mauchly, Betty Snyder Holburton, Fran Bilas Spence, Marlyn Wescoff Meltzer, and Ruth Lichterman Titlebaum – Hired as human computers, then assigned to the ENIAC – Developed techniques we still use, like breakpoints