Logic

Whilst its only recapped on in some of the lectures, it assumes knowledge from the engineering module, which the computer science Computer Organisation and Architecture (CS132) also covers.

A fair bit of this information is already in CS132 Logic Page. There are some engineering specific things, and stuff that's just handy to have on one page.

Boolean Algebra Laws

There are several laws of boolean algebra which can be used to simplify logic expressions:

Name	AND form	OR form
Identity Law	$1 A = A$	$0 + A = A$
Null Law	$0 A = 0$	$1 + A = 1$
Idempotent Law	$AA = A$	$A + A = A$
Inverse Law	$A \overset{ˉ}{A} = 0$	$A + \overset{ˉ}{A} = 1$
Commutative Law	$A B = B A$	$A + B = B + A$
Associative Law	$(A B) C = A (BC) = A BC$	$(A + B) + C = A + (B + C) = A + B + C$
Distributive Law	$A + BC = (A + B) (A + C)$	$A (B + C) = A B + A C$
Absorption Law	$A (A + B) = A$	$A + A B = A$
De Morgan's Law	$\overline{A \cdot B} = \overset{ˉ}{A} + \overset{ˉ}{B}$	$\overline{A + B} = \overset{ˉ}{A} \cdot \overset{ˉ}{B}$

Can go from AND to OR form (and vice versa) by swapping AND for OR, and 0 for 1

Most are fairly intuitive, but some less so. The important ones to remember are:

$A + BC = (A + B) (A + C)$
$A (B + C) = A B + A C$
$A (A + B) = A$
$A + A B = A$

Latches

SR Latch

When $S$ is asserted, $Q$ goes high.
When $R$ is asserted, $Q$ goes low.
When both are de-asserted (low and low), $Q$ holds its value
When both are asserted (high and high), $Q$ and $\overline{Q}$ goes low (not intended!)

D latch

Passes through the $D$ input whenever $C L K$ is high, and hold when $C L K$ is low.

D Flip Flop

Will copy the $D$ input to the $Q$ output at rising edges of $C L K$ . Bit storage.

Computer Systems Engineering Notes