C2 - Binary Number and Digital Logic

Analog

Signal

• Uncountable infinite number of values
• e.g. sound, visual, current

System

• Its signal is manipulated as a continuously changing quantity
• e.g. human, telephone, AM/FM, analog TV, film camera

In 1876, Alexander Graham Bell invented telephone

Degradation

• Attenuation (change in amplitude)
• Distortion (change in shape)
• Noise (addition of noise)

Signal to Noise Ratio (SNR)

• Larger SNR $\to$ minimize noise error

Digital

• Discrete values at discrete time/space
• Reproducible with threshold detection and coding

George Boole invented Boolean Algebra

In 1936, Alan Turing proposed the Turing Machine

In 1937, Claude Shannon applied boolean algebra to simplify telephony switching system

Digital TV

• No snowy pictures
• No ghosting

HK ~ 2007
USA ~ 2009

Binary Logic

Gate	Formula	Symbol
NOT	$B=\bar{A}$
AND	$C=A\cdot B$
OR	$C=A+B$

Digital Notations

\begin{flalign} &2^{10} = 1\,\mathrm{K} \\ &2^{20} = 1\,\mathrm{M} \\ &2^{30} = 1\,\mathrm{G} && \end{flalign}

$1\mathrm{k}=10^3=1,000$
$1\mathrm{K}=2^{10}=1,024$