Samenvatting Basis Algoritmiek & Informatica

BAI SAMENVATTING
Basis Algoritmiek & Informatica
Richard Reijerse
21-10-2020

Inhoud
1. Getallen en representaties .............................................................................................................. 2
Positietalstelsels .................................................................................................................................. 2
Algoritmiek .......................................................................................................................................... 3
Datastructuren .................................................................................................................................... 5
Logica ................................................................................................................................................... 6
Verzamelingen ..................................................................................................................................... 7
2. Oefeningen .................................................................................................................................... 12
Getallen en representaties ................................................................................................................ 12
Algoritmiek ........................................................................................................................................ 13
Logica ................................................................................................................................................. 13
Verzamelingen ................................................................................................................................... 14

, 1. Getallen en representaties

Positietalstelsels
formule klmb = k x b2 + l x b1 + m x b0



bij een getal ‘b’ van 4 zijn het dus alleen
de getallen 0 t/m 3
!
decimale stelsel Basis 10 (symbolen 0..9)
123 = 1 x 102 + 2 x 101 + 3 x 100
123 = 1 x 100 + 2 x 10 + 3 x 1

binaire stelsel Basis 2 (symbolen 0 en 1)
1012 = 1 x 22 + 0 x 21 + 1 x 20
1012 = 1 x 4 + 0 x 2 + 1 x 1 (5 in dec)

octale stelsel 3 bits per 1 positie

74
= 0010010102
= 001 001 0102
= 1128

hexadecimaal 4 bits per 1 positie

74
= 010010102
= 0100 10102
= 4A16

Toepassing:
 Kleurcodes
 URL’s
 Geheugenadressen

negatief decimaal  2’s compliment Decimaal: Binair (8 bits):
77  0100 1101 stap0: binair getal
1011 0010 stap1: inverteer bits
-77  1011 0011 stap2: tel 1 op
2’s compliment  negatief Decimaal: Binair (8 bits):
decimaal -77  1011 0011 stap0: binair getal
0100 1100 stap1: inverteer bits
77  0100 1101 stap2: tel 1 op
rekenen met 2’s compliment Decimaal: 123 – 77 = 123 + (-77) = 46

Binair (8 bits):
123  0111 1011
-77 +  1011 0011 +
46  0010 1110