Different Numeration SystemPelbagai Sistem Pernomboran

Minggu 2

Sistem Pernomboran LainAsas dalam sistem pernomboran mewakili bilangan simbol yang digunakan dalam pengumpulanSemua nombor ditulis dalam bentuk kuasa mengikut asasnyaUntuk asas lebih dari 10, simbol lain boleh diperkenalkan

Bilangan simbol

AsasSimbolKaedah PengumpuanNotasiDua0, 11011duaTiga0,1,2102tigaEmpat0,1,2,323empatLima0,1,2,3,421limaEnam0,1,2,3,4,515enam

AsasSimbolKaedah PengumpulanNotasitujuh0,1,2,3,4,5,614tujuhlapan0,1,2,3,4,5,6,713lapanSembilan0,1,2,3,4,5,6,7,812sembilanSepuluh0,1,2,3,4,5,6,7,8,911sepuluhsebelas0,1,2,3,4,5,6,7,8,9,t10sebelas

Do you see a pattern?Bilangan simbol yang digunakan untuk Asas 5 (grouping by 5)Asas 10Asas 2Asas 11Asas 12Asas b

Menukarkan Asas: Asas b Asas 10Tuliskan angka dalam expanded notationContoh: Tukar setiap berikut kepada asas 10:1011.01dua1011.01empat1011.01lima

Cuba selesaikan:Tukarkan kepada asas sepuluh.1110012 12345 30762854297652349

Asas 10 Asas b Contoh: Tukar 42 kepada asas dua.

1. Dengan menggunakan carta nilai-tempat42 = 32 + 8 + 2 (expanded notation) = 25 + 23 + 21

252423222120101010

Dgn Menggunakan repeated division2 ) 42 2 ) 21 tiada baki - 0 2 ) 10 baki - 1 2 ) 5 tiada baki - 0 2 ) 2 baki - 1 2 ) 1 tiada baki - 0 0 baki - 1

Read upwards101010

Latihan LanjutanTukarkan 52 (by expanded notation) kpd: a) Asas tigab) Asas empatc) Asas limaTukarkan 67 (by repeated division) kpd a) Asas tujuhb) Asas lapanc) Asas dua-belas

Problem Solvingpage 133Suppose you need to purchase 1000 name tags and can buy them by the gross (144), the dozens (12) or individually. The name tags cost RM0.50 each, RM4.80 per dozen and RM50.40 per gross. How much should you order to minimize the cost?

Converting between Numeration SystemTo convert from base b numeration system to Hindu-Arabic (decimal) numeration system -> write the base b numeral in expanded form & then simplify.To convert from Hindu-Arabic numeration system to base b numeration system -> perform repeated division by b & then read the remainders from bottom-up.

Problem Set 3.3 (page 133)Level 1 Qn 1 & 3

Level 2Qn 48, 51, 52, 56

Binary Numeration SystemBase TwoCompare the binary system with the light switch; on-off, on = 1; off = 0 a good example of a two state deviceRefer to figure 3.5 (page 135) for the binary numerals.

Converting the binary systemWhat is 1110two ?

What is 53 in binary system ?

ASCII (American Standard Code for Information Interchange), 1964In the computer, each switch is a bit ( a 1 or 0)A group of these 8 switches is lined up to form a byte, i.e. any number from 0 to 111111112 = 255tenThe code used to represent every letter & symbol (see Table 3.8, page 137)Example: c = 99 (01100011, off-on-on-off-off-off-on-on); a = 97 (01100001); t = 116 (01110100)

Binary ArithmeticAdditionMultiplication

x01000101

+010011110

Exercise112 + 1012

112 x 1012

Problem Set 3.4Level 11, 3, 4, 5, 6, 13, 15, 17, 28, 29, 30Level 232, 34, 36, 3839 - 46

Tutorial 1bSome students say that studying different number bases is a waste of time. Explain the value of studying base four, for example, in helping you to understand our decimal system.What is a real-world use for number base 2 and 16?