1.2 Number Bases, SPM Paper 1 (Short Questions)


Question 8:
Express 110101012 as a number in base eight.

Solution:




Question 9:
Express 100001102 as a number in base eight.

Solution:




Question 10:
Given  h 8 = 10111 2 , where h is an integer, find the value of h.

Solution:




Question 11:
Express each of the following as a number in base two.
(a) 26 + 24 + 1
(b) 25 + 23 + 2 + 20

Solution:
(a) 2 6 + 2 4 +1 = 1 _ × 2 6 + 0 _ × 2 5 + 1 _ × 2 4 + 0 _ × 2 3 + 0 _ × 2 2 + 0 _ × 2 1 + 1 _ × 2 0 = 1010001 2

(b) 2 5 + 2 3 +2+ 2 0 = 1 _ × 2 5 + 0 _ × 2 4 + 1 _ × 2 3 + 0 _ × 2 2 + 1 _ × 2 1 + 1 _ × 2 0 = 101011 2



Question 12:
State the value of the digit 2 in the number 324175 , in base ten.

Solution:

 

3

2

4

1

7

Place Value

54

53

52

51

50

Value of the digit 2
= 2 × 53
= 250


Question 13:
101102 + 1112 =

Solution:


Alternatively, use a scientific calculator to get the answer directly.


Question 14:
1100102 – 1112 =

Solution:


Alternatively, use a scientific calculator to get the answer directly.

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