Question 8:
Express 11010101_{2} as a number in base eight.
Solution:
Express 11010101_{2} as a number in base eight.
Solution:
Question 9:
Express 10000110_{2} as a number in base eight.
Solution:
Express 10000110_{2} as a number in base eight.
Solution:
Question 10:
$\text{Given}{h}_{8}={10111}_{2},\text{where}h\text{isaninteger,findthevalueof}h\text{.}$
Solution:
$\text{Given}{h}_{8}={10111}_{2},\text{where}h\text{isaninteger,findthevalueof}h\text{.}$
Solution:
Question 11:
Express each of the following as a number in base two.
(a) 2^{6} + 2^{4} + 1
(b) 2^{5} + 2^{3} + 2 + 2^{0}
Solution:
$\begin{array}{l}\text{(a)}\\ {2}^{6}+{2}^{4}+1\\ =\underset{\_}{1}\times {2}^{6}+\underset{\_}{0}\times {2}^{5}+\underset{\_}{1}\times {2}^{4}+\underset{\_}{0}\times {2}^{3}+\underset{\_}{0}\times {2}^{2}+\underset{\_}{0}\times {2}^{1}+\underset{\_}{1}\times {2}^{0}\\ ={1010001}_{2}\end{array}$
$\begin{array}{l}\text{(b)}\\ {2}^{5}+{2}^{3}+2+{2}^{0}\\ =\underset{\_}{1}\times {2}^{5}+\underset{\_}{0}\times {2}^{4}+\underset{\_}{1}\times {2}^{3}+\underset{\_}{0}\times {2}^{2}+\underset{\_}{1}\times {2}^{1}+\underset{\_}{1}\times {2}^{0}\\ ={101011}_{2}\end{array}$
Express each of the following as a number in base two.
(a) 2^{6} + 2^{4} + 1
(b) 2^{5} + 2^{3} + 2 + 2^{0}
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 32417_{5} , in base ten.
Solution:
Value of the digit 2
= 2 × 5^{3}
= 250
State the value of the digit 2 in the number 32417_{5} , in base ten.
Solution:

3 
2 
4 
1 
7 
Place Value 
5^{4} 
5^{3} 
5^{2} 
5^{1} 
5^{0} 
= 2 × 5^{3}
= 250
Question 13:
10110_{2} + 111_{2} =
Solution:
Alternatively, use a scientific calculator to get the answer directly.
10110_{2} + 111_{2} =
Solution:
Alternatively, use a scientific calculator to get the answer directly.
Question 14:
110010_{2} – 111_{2} =
Solution:
Alternatively, use a scientific calculator to get the answer directly.
110010_{2} – 111_{2} =
Solution:
Alternatively, use a scientific calculator to get the answer directly.