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Samenvatting Basis Algoritmiek & Informatica
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BAI SAMENVATTINGBasis Algoritmiek & Informatica
Richard Reijerse
21-10-2020
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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
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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
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