Microelectronics Flashcards
How to implement Duality Principle
In a boolean Equation:
- ) change all 0’s to 1’s and change all 1’s to 0’s
- ) change all AND’s(⋅) to OR’s(+) and change all OR’s(+) to AND’s(⋅)
DO NOT CHANGE THE COMPEMENTED/NON-COMPLEMENTED VARIABLES (If its A, let it stay as A; if its B’, let it stay as B’)
Founder of Boolean Algebra
George Bool
(DEC) of fractional/decimal numbers into (HEX),(OCT),(BIN)
- ) Multiply (2 for BIN, 8 for OCT, 16 for HEX) to the Base 10 fractional number (use Base 10 multiplication)
- )the result of 1.) is A . B (A is the whole number, B is the Fractional)
- ) Append A next to the floating point (ex. 0.A)
- ) Repeat Step 1, but use B as the fractional number multiplied to 2, 8, or 16
- ) Result’s Whole number is appended next to the previous whole number
- ) Repeat until the fractional part becomes 0
The principle that governs how machines perform subtraction
N’s Complement (2’s Complement for binary)
Given a minuend and subtrahend, how is n’s complement subtraction performed?
Minuend + [N’s Complement of Subtrahend]
If sum overflows, discard overflowed digit, remainder is the difference (positive number)
If sum does not overflow, perform n’s complement on it, anfd append negative sign to get the difference (negative number)
The Inventor of the Hollerith Table
Herman Hollerith
Herman Hollerith made punch cards that used the Hollerith table for a company he organized called _________, that later became _________
Tabulating Machine Corporation (1896) becomes International Business Machines (IBM, 1924)
The Hollerith had ___ columns, and ___ rows
80 columns, 12 Rows
the 12 rows of the Hollerith table are composed of ___ Digit Rows and ___ Zone Rows
9 Digit Rows
3 Zone Rows
If a Numerical character was to be encoded into the hollerith table, the column that stores this character will have ___ punch/es in the ____ Row/s
1 punch in the Digit Row
If an Alphabetic character was to be encoded into the hollerith table, the column that stores this character will have ___ punch/es in the ____ Row/s
2 punches in Digit and Zone Row (1 each)
If a Special Character was to be encoded into the hollerith table, the column that stores this character will have ___ punch/es
1 or 2 or more punches
EBCDIC stands for ______
Extended Binary Coded Decimal Interchange Code
EBCIDIC is IBM Proprietary. What does that mean?
Only IBM Machines have the capability of using the EBCDIC Code
EBCDIC is in _____ Format, and is a/an ___ bit code
Binary Coded Decimal(BCD), 8 bit
ASCII stands for _____
American Standard Code for Information Interchange
ASCII uses __ bits to represent ___ Characters
7 bits to represent 128 characters
ASCII’s 128 Characters are composed of ___ Printable Characters and ___ Non-Printable Characters
94 Printable, 34 non-printable
Idempotent Law
X + X = X
X ⋅ X = X
Involution Law
(X’)’ = X
Complimentary Law
X + X’ = 1
X ⋅ X’ = 0
Commutative Law
X + Y = Y + X
X ⋅ Y = Y ⋅ X
Associative Law
(X + Y) + Z = X + (Y + Z)
X ⋅ Y) ⋅ Z = X ⋅ (Y ⋅ Z
Distributive Law
X(Y +Z) = X⋅Y + X⋅Z
X + Y ⋅ Z = (X + Y) ⋅ (X + Z)
Duality Operator
(X + Y + Z + …)ᴰ = X⋅Y⋅Z
(X⋅Y⋅Z)ᴰ = X + Y + Z
Simplification Theorem:
X⋅Y + X⋅Y’ = ?
X⋅Y + X⋅Y’ =
X
Simplification Theorem:
A⋅(A + B + C + … ) = ?
A⋅(A + B + C + … ) =
A
Simplification Theorem:
X + X⋅Y = ?
X + X⋅Y =
X
Simplification Theorem:
(X +Y’)⋅Y = ?
(X +Y’)⋅Y =
X⋅Y
Simplification Theorem:
(X + Y)⋅(X +Y’) = ?
(X + Y)⋅(X +Y’) =
X
Simplification Theorem:
X⋅(X +Y) = ?
X⋅(X +Y) =
X
Simplification Theorem:
X⋅Y’ + Y = ?
X⋅Y’ + Y =
X + Y
Multiplying out & Factoring:
(X +Y) ⋅ (X’ + Z) = ?
(X +Y) ⋅ (X’ + Z) =
X⋅Z + X’⋅Z
Multiplying out & Factoring:
X⋅Y + X’⋅Z = ?
X⋅Y + X’⋅Z =
X + Z) ⋅ (X’ + Y
Consensus Theorem:
X⋅Y + Y⋅Z + X’⋅Z = ?
X⋅Y + Y⋅Z + X’⋅Z =
X⋅Y + X’⋅Z
Consensus Theorem:
(X + Y) ⋅ (Y + Z) ⋅ (X’ + Z) = ?
(X + Y) ⋅ (Y + Z) ⋅ (X’ + Z) =
X + Y) ⋅ (X’ + Z
A product of ‘n’ Literals or Variables
Minterm
The Summation of minterms form a ____
Minterm Expansion
or
Sum of Products (SOP)
A boolean function can be expressed as the summation of its minterms or in SOP form:
F(x,y,z) = ∑m(1,2,3,…)
now, if F = 1, then _______ of the minterms are also equal to ___
at least one of the minterms are also equal to 1
A Summation of ‘n’ Literals or Variables
Maxterm
The Product of Maxterms form a ____
Maxterm Expansion
or
Product of Sums (POS)
A boolean function can be expressed as the product of its maxterms or in POS form:
F(x,y,z) = ∏M(1,2,3,…)
now, if F = 0, then _______ of the minterms are also equal to ___
at least one of the maxterms are also equal to 0
the Minterm or Maxterm of the first entry in a truth table always start with the subscript of ____
0
Minterm - Maxterm Conversions:
Mₙ = ?
Mₙ =
mₙ’
Minterm - Maxterm Conversions:
mₙ = ?
mₙ =
Mₙ’
given only 3 variables ( 2³ = 8, so terms involved are 0,1,2,3,4,5,6,7) Convert in terms of maxterms:
m₀ + m₁ + m₂ + m₃ = ?
m₁ + m₂ + m₃ + m₄ =
M₄M₅M₆M₇
given only 3 variables ( 2³ = 8, so terms involved are 0,1,2,3,4,5,6,7)
(m₀ + m₁ + m₂ + m₃)’ = ?
(m₀ + m₁ + m₂ + m₃)’ =
m₀’m₁’m₂’m₃’
given only 3 variables ( 2³ = 8, so terms involved are 0,1,2,3,4,5,6,7)
(M₄M₅M₆M₇)’ = ?
(M₄M₅M₆M₇)’ =
M₄’ + M₅’ + M₆’ + M₇’
A product/sum of inputs that are deemed impossible to occur, or the output of that specific set of inputs is not needed will produce a minterm/maxterm considered as
a ______
Dont Care Term
If an output is true, it has an output of ‘1’
If an output is false, it has an output of ‘0’
If an output is useless/impossibe/not needed/dont care, it has an output of ‘__’
X
Minterm Expansion Expression with Dont Care Terms
∑m(,,,…) + ∑d(,,,…)
Maxterm Expansion Expression with Dont Care Terms
∏M(,,,…) + ∏D(,,,…)
In a K-Map, any two adjacent squares have ___ variables in common
no variables in common
The code used that enables the K-Map to employ the non-common variables of any adjacent square
Grey Code
For an n-variable K-map (ex. 4 variable k-map), how many variables does the value of one square represent/depend upon?
n variables (in the example, 4 variables)
For an n-variable K-map (ex. 4 variable k-map), how many variables does the value of two adjacent squares represent/depend upon?
n-1 variables (in the example, 3 variables)
For an n-variable K-map (ex. 4 variable k-map), how many variables does the value of 2^a adjacent squares represent/depend upon?
(n-a) variables
For an n-variable K-map (ex. 4 variable k-map), how many variables does the value of n adjacent squares represent/depend upon?
none (whole K-Map is grouped, Value of the function, regardless of the input, is automatically 1)
When grouping 1’s (if minterm expansion is used), the number of squares allowed in a group must be ______
A Power of 2 (2^a, a is any integer)
A Group in a k-map which is not completely enveloped by a larger group, but its squares can be part of any other group
Prime Implicant
No matter how we group 1’s or 0’s in a k-map, this group will always have at least one square that uniquely belongs to this group alone
Essential Prime implicant
Assuming minterm expansions are used in a k-map, if some minterms, that represent one square each, has a value of 1, the square that that minterm represents is denoted with a _____
1
Assuming maxterm expansions are used in a k-map, if some maxterms, that represent one square each, has a value of 0, the square that that maxterm represents is denoted with a _____
0
Assuming either minterm or maxterm expansions are used in a k-map, if some minterms/maxterms, that represent one square each, is a dont care term, the square that that minterm/maxterm represents is denoted with a _____
X
In a K-map, are dont care terms(X) also included in the Grouping?
Yes
when Grouping in a k-map, is a group that only has dont care terms (X) valid?
no
The Logic gate that determines if the sum of the inputs is even or odd
Exclusive-OR Gate (XOR)
When The output of the XOR Gate is 0, the sum of its inputs is (even/odd)
even
When The output of the XOR Gate is 1, the sum of its inputs is (even/odd)
odd
The two universal gates (gates that can form any other gate using just themselves)
NAND and NOR
Any gate can be formed with only NAND gates, or only with NOR gates
Half-Adders / Full-Adders have two output bits; the ___ bit and the ___ bit
Sum and Carry
Given the inputs X and Y, What is the boolean expression for the Sum bit of a Half-Adder Circuit
S = X ⊕ Y
Given the inputs X and Y, What is the boolean expression for the Carry bit of a Half-Adder Circuit
C = X ⋅ Y
The inputs of a Half-Adder are called _____
Augend and Addend
A Full Adder Circuit has ___ inputs and ___ outputs
3 inputs, 2 outputs
A Full Adder consists of ______
Two Half Adders
When the inputs of the Full Adder Circuit are X, Y and Z, Z represents the ______
Carry from a lower significant position
Given the inputs X, Y and Z, What is the boolean expression for the Sum bit of a Full-Adder Circuit
S = (X ⊕ Y) ⊕ Z
Given the inputs X, Y and Z, What is the boolean expression for the Carry bit of a Full-Adder Circuit
C = (X⋅Y) + Z⋅(X ⊕ Y)
Full Adders can be cascaded into _______
Ripple Carry Adders
For a Ripple Carry adder with ‘n’ bits, the number of Full Adders needed is ______
‘n’ #Full adders
It is considered as the basic storage unit, and is the building block of a Flip-Flop
Latch
The Two Inputs of an SR-Latch are ____ and ____
Set and Reset
Truth Table of an SR Latch
S | R | Remarks --------------------- 0 | 0 | retain 0 | 1 | reset 1 | 0 | Set 1 | 1 |Undefined
When Both Set and Reset have a value of ‘1’, the situation is called _________
Race Condition (Circuit is confused, whether to set or reset, so it becomes a race to see which one of the two inputs become value ‘1’ first)
A D-Latch has ___ Input/s
only one
When input D in a D-latch is ‘1’, the output ____
Sets (1)
When input D in a D-latch is ‘0’, the output ____
Resets (0)
Latches are circuits (with/without) clocks
without clocks
Bistable circuits built from latches, and uses a clock
Flip-Flop
Flip-Flips have __ inputs and ___ outputs
2 Inputs (J and K), 2 outputs (Q and Q’)
When the Inputs of a JK Flip Flop are:
J = 0 , K = 0
the next state of the output (Q(t+1)) is ______
Q(t) (Retain previous state)
When the Inputs of a JK Flip Flop are:
J = 0 , K = 1
the next state of the output (Q(t+1)) is ______
0 (Reset)
