Binary and numbers
Ranges
unsigned:
signed magnitude:
has both positive and negative 0
2’s compliment:
ieee 754 32bit floating point
1 bit sign, 8 bits exponent, 23 bit mantissa (decimal) → 1.mantissa
K MAP
How to evaluate
- Group 1’s and X’s by powers of 2, including 1
- Each group’s expressions use AND
- Join groups with OR
Transistors
N-type
open with input greater than 0 aka acts as a circuit when there’s input
P-type
Open with input 0
Circuits
Transistor count
2n + 2 transistors for n inputs because corresponding NAND / NOR with an inverter
Decoder
Turns on one of its outputs via some selector bits
Mux
Passes through one of its inputs based on its selector bits
Sequential
RS Latch
- stores a bit
Table
Sets to 1 when S is 0 Resets to 0 when R is 0 11 - retain 00 - invalid
Composition
Two NAND’s each with its output as one of the other’s input. Has R and S input.
Gated D Latch
- Level triggered Two NAND’s with DATA negated into the top one. Data and WE go into both. Feeds into an RS.
D Flip Flop
- Rising edge triggered
Registers
- D Flip Flop
- Edge triggered
Memory
- Gated D latches
- Level triggered
Addressability
Addressability - space each address holds Address space - number of addresses Total memory = addressability * address space
Compilation
Preprocessing Compilation Assembler Linking
What they do
Preprocessing - copy-pastes code into single file, does macros, etc Compilation - C into assembly Assembler - Assembly into machine code Linking -