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

Solution:
$\begin{array}{l}\text{(a)}\\ 2^6+2^4+1\\ =\underset{\_}{1}\times 2^6+\underset{\_}{0}\times 2^5+\underset{\_}{1}\times 2^4+\underset{\_}{0}\times 2^3+\underset{\_}{0}\times 2^2+\underset{\_}{0}\times 2^1+\underset{\_}{1}\times 2^0\\ ={1010001}_2\end{array}$

$\begin{array}{l}\text{(b)}\\ 2^5+2^3+2+2^0\\ =\underset{\_}{1}\times 2^5+\underset{\_}{0}\times 2^4+\underset{\_}{1}\times 2^3+\underset{\_}{0}\times 2^2+\underset{\_}{1}\times 2^1+\underset{\_}{1}\times 2^0\\ ={101011}_2\end{array}$

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

Solution:


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.

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

Solution:

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

Solution:

Question 10:
$\text{Given }{h}_8={10111}_2,\text{ where }h\text{ is an integer, find the value of }h\text{.}$

Solution:

Question 5:
Solution:

	4	3	1	5
Place Value	53	52	51	50

= 75

Question 6:
Solution:

53	52	51	50
1	0	2	05