Introduction, gates, and binary stuff Flashcards
4 Number types
- Decimal/Base 10
- Binary
- Hexadecimal
- octal
num type that we use
decimal/base 10
everything is stored in
binary
binary base
2
octal base
8
hexadecimal base
16
stuff stored in binary
- characters ( ascii )
- sound ( digitized )
- picture ( RGB )
Binary Coded Decimal notation
Binary encodings of decimal numbers where each digit is represented by a fixed number of digits, usually being 4 or 8.
convert binary to octal
group in 3s
convert binary to hexadecimal
group in 4s
convert from decimal
divide by specific base, keeping track of remainders, then write in reverse order
0 and 1 is represented by
voltage level depending on chip type
our family of chips
TTL chips
TTL chips low voltage ( 0 )
0-0.8 volts
TTL chips high voltage ( 1 )
2-5 volts
active high logic means
1 = true
0 = false
active low logic means
0 = true
1 = false
which logic do we usually use
active high logic ( true = 1 , false = 0 )
the multiplication symbol in binary algebra represents
“and”
the addition symbol in binary algebra represents
“or”
AND gate code
7408
AND gate formula
F = XY ( f is true when x and y are high )
OR gate code
7432
OR gate formula
F = X + Y
NAND gate code
7400
NAND gate formula
F = ( XY )’
NOR gate code
7402
NOR gate formula
F = ( X + Y )’
NOT gate code
7404
NOT gate formula
F = X’
The NOT gate does what
inverts
NAND gate has the
lowest numbered code
All TTL chips are numbered
74XX or 74XXX ; 54… represents same chip but designed for the military
all other gates can be built using only
NAND gates
binary circuit
0 or 1 inputs, 0 or 1 output
binary circuits can be built using only
NAND gates
a digital computer may be built using only
NAND gates
NOT gate is an
inverter
EXCLUSIVE OR gates mean
they do not include both like traditional OR gates do
EXCLUSIVE OR gate code
7486
EXCLUSIVE NOR gate code
74266
EXCLUSIVE OR gate formula
F = X’Y + XY’
F = X (+) Y
EXCLUSIVE NOR gate formula
F = XY + X’Y’