CSE Exam 4

Name of gate, when is Y = 1

XOR, When A and B are different

Name of gate, when is Y = 1

NAND, When A = 0 or B = 0

Name of gate, when is Y = 1

NOR, When A = 0 and B = 0

Name of gate, when is Y = 1

XNOR, When A and B are the same

A logic circuit is composed of (4 things)

Inputs

Outputs

Functional Specification

Timing Specification

Two types of circuits, two attributes of each (Memory, Outputs determined by)

Combinational Logic

-Memoryless

-Outputs determined by current values of inputs

Sequential Logic

-Has memory

-Outputs determined by previous and current values of inputs

Minterm:

Product that includes all input variables

Maxterm:

Sum that includes all input variables

SOP Form

A sum (OR +) of products (AND *) Where the output is TRUE

POS Form

A product (AND *) of sums (OR +) where the output is FALSE.

A + A̅ =

1

A + 1 =

1

A * A̅ =

0

A + AB =

A

A * 1 =

A

A + BC =

(A+B) * (A+C)

AB + AB̅ =

AA

A + A̅B =

A + B

Three attributes of digital building blocks (Gates, multiplexers, decoders, registers, arithmetic circuits, counters, memory arrays, logic arrays)

Hierarchy, modularity, and regularity

Easiest (preferred) gates to create

NOT, NAND, NOR

Rules of Combinational Composition (3)

-Every element is combinational

-Every node is either an input or connects to exactly one output

-The circuit contains no cyclic paths

Create a decoder from a truth table : procedure

Write SOP boolean expression, create structure with every variable and it’s complement, combine them with AND gates to form every minterm in the SOP expression
N inputs, 2^N outputs

Create a multiplexer from a truth table: procedure

Write simplified boolean expression, choose selection variable(s), replace non-selection variables with numbered inputs