CS10001 – Understanding Computing Based Technologies: Binary Foundations
A bit is a uni t of storag e t hat c an have a val ue of ‘1’ or ‘0’. Th e process of represent ing inform ation
in bi nary req uires tha t there be en ou gh bits to un iq uely distin gu ish o ne th ing from anoth er.
For examp le our number system (base-10) al lo ws us to represent ten d ifferent quant it ies (e.g. zero –
nin e) using a un iq ue symb ol (e.g. 0-9) for ea ch o f these t en di fferent qu an tities. T o re present larger
quant it ies we use a system th at al lows us to repr esent a l arger quan tity b y p la c in g one o f the base
dig its in a h ig her order position ( i.e. 10 represent th e qua nt ity 10 bec ause the higher order positio n
ind ica tes th e va lue of the base-di gi t m ulti p li ed by 10) . In th is fash ion we can represent a n infinite
number of qu an tities simp ly by a dd in g hi gh er or der p osition to this system. (i.e. 10 0 represents one
hundred, 150 0 represents one thousan d a nd five hundr ed). T hus a dding a h igher order positio n to
a base-10 nu mb er i ncre ases the max imu m v al ue th at ca n be represented by a pow er of 10. If you
are li mite d to 2 p ositions in the b ase-10 nu mb er system you ca n on ly un ique ly id entify 1 02 = 10 0
thi ngs using the i dentifiers 00- 99.
Everythin g in a c om pu ter is represented i n the base-2 number system (also ca l le d the binary
number system) T he un ique symbols in this number system are 0 & 1. An infinite nu mb er o f u ni qu e
val ues can a lso b e re presented in the base-2 nu mb er system but ea ch h ig her order position
in creases the maxi mu m val ue th at can be represented by a power o f 2 instea d o f 1 0. If yo u use
eig ht b its to en code some thing you ca n un ique ly id entify at most 28 = 256 th in gs usin g the
ide nt if iers 00000000 - 1 1111111.
A byte is a c ombin at ion o f e ig ht bi ts. Byt es store characters (regu lar or speci al) a nd di gits in u nique
co mb i nations; o ne c har ac ter at a t im e. Va lu es are en co de d using a di fferent system than th e
en co di ng used for representin g text.
Example: Represent th e digit ‘8’ in A SCII binary usin g 1 byte of stora ge.
0 0 1 1 1 0 0 0
Example: Represent th e va lue eight in base-2 binary form using 1 byt e o f storag e.
0 0 0 0 1 0 0 0
___ ___ ___ ___ ___ ___ ___ ___
27 26 25 24 23 22 21 20
Note: We use unique co mb in at io ns of our al ph abet to prod uc e words. Whe n stori ng
text ea ch by te en codes a single let ter using a byte b ased encodi ng system ca ll
ASCII (Ameri ca n Sta nd ard Code for Inf orm ation Inter ch an ge). Even a spa ce m ust
be en co de d and the ASCII binary code for a space/bl ank is 00100000. Th us the
Eng l ish word “system” co ntai ns six le tters and wou ld require six bytes of storage in a
co mp uter.
Th ere is no such conc ep t as senten ces, paragraphs, a nd pa ges for data storage in a c omputer .
Altho ug h t he data tha t is stored is ofte n text, whic h we crea te d as sente nce, p aragraphs, and p ag es,
insi de the c omp uter ea ch ch ara cter of text takes up pr ec isely 1 byte of spa ce . So, we discussing
data storage we speak of th e quant ity of byt es using th e stan dard prefix-mu lt ip liers used thro ug h-ou t
scie nce an d engineerin g (e.g. kilo, mega, g ig a, tera , p eta ,…). I n I T and d ata storage, mu lt ip liers
are def ined in p owers of 2 from 210 to 280, pro ceed in g in incremen ts of t en orders of m agni tud e (210
or 1,024, also known as a Kiloby te). Th ese multipli ers are denoted in th e f ollowing ta ble.
Th e co mput er uses the follow in g pref ixes where re ferring to stor age c ap ab il ity:
