Chapter 2 Flashcards
Convert binary to decimal
101011
10011
1001001
43
19
73
Convert decimal to binary:
35
67
14
100011
1000011
1110
Conversion method for twos complement.
- Change the sign to get the magnitude of the number, invert the binary number and add 1
- Convert to decimal.
Transistor based design
nMOS conducts on 1 and not on 0
cMOS does not conduct on 1, but does connect on 0
Boolean algebra symbols
Not ‘
Or +
And &
Literal
An appearance of a variable in either true or complemented form a’ or a
Variable
Represents a quantity (1 or 0)
Product term
Product of literals
Sum of products
An equation written as an ORing of product terms
abc’ + abc
Not correct form:
(ab + ab’)’
Communicative property
a + b = b + a
a * b = b * a
Distributive
a * ( b + c ) = a * b + a * c
a + (b * c) = (a + b)*(a + c)
Associative
(a + b) + c = a + (b + c)
a * b) * c = a * (b * c
Identity
a + 0 = a
1 * a = a
Complement
a + a’ = 1
a * a’ = 0
Idepotent
a + a = a
a * a = a
Involution Law
(a’)’ = a
DeMorgan’s Law
(a + b)’ = a’b’
(ab)’ = a’ + b’
Canonical Form
The standardized representation of a Boolean function
Minterm
Product term whose literals include every variable in the function exactly once
Sum - of - minterms
An equation in sum-of-products term where every term is a minterm
Decoder
A high level building block commonly used in digital circuits. A decoder decodes inputs n-binary number by setting exactly one of the decodes 2^n outputs to 1. If e = 0 -> all outputs = 0
Inputs: i0 i1 (selectors, decides which output should be 1) e (enabler, 1if using decoder.)
Outputs: one output, selected by the selectors, is 1, else they are all 0’s
Encoder
The opposite functionality of a decoder has n number of inputs and log^2(n) number of outputs. Exactly 1 input is assumed to be 1 at a time. Priority decoder deal with more then 1 input being 1 at a time
Muxes
A m X 1 mux has m data inputs and 1 data output and allows only one input to pass through to that input.
