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

  1. Group 1’s and X’s by powers of 2, including 1
  2. Each group’s expressions use AND
  3. 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 -

Stack Subroutine