Lec1. Numeral System

Question 1

Explain each term: a = dq + r

Answer 1

a is the dividend
d is the divisor
q is the quotient
r is the remainder

Question 2

what is a div d?

Answer 2

q

Question 3

what is a mod d?

Answer 3

r

Question 4

True/False: Base b expansion: b > 1 and n ≥ 0

Answer 4

False. b must be larger than 1 and n must be larger than 0 since (0)b = 0 –> not giving a unique case

Question 5

True/False: if the base b = 7, a possibilities is ak = 8

Answer 5

False, ak < b

Question 6

What is the domain and codomain of div?

Answer 6

div: N x N* -> N
(a,d) -> q

div ((a,d)) = q or a div d = q

Question 7

What is the domain and codomain of mod?

Answer 7

mod: N x N* -> N
(a,d) -> r
mod((a,d)) or a mod d = r

Question 8

True/False: r is the number expansion of base b

Answer 8

true

Question 9

True/False: 0 ≤ r ≤ d

Answer 9

false -> 0 ≤ r ≤ d-1

Question 10

A digit in binary notation is called ____

Answer 10

bit

Question 11

A ___ which consists of 8 bits, can be represented by 2 digit-hexadecimal number

Answer 11

byte