Number Bases

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 … Read more

Question 1: Express 2058 as a number of base five. Solution: 2058 = 2 × 82 + 0 × 81+ 5 × 80 = 13310   Question 2: State the value of the digit 6 in the number 16238, in base ten. Solution: Identify the place value of each digit in the number first. 1 … Read more

(F) Addition and Subtraction of Two Numbers in Base Two 1. In the addition of two numbers in base two, the following rules applied:     02 + 02 = 02   02 + 12 = 12   12 + 02 = 12   12 + 12 = 102   12 + 12 + 12 = 102 + 12 = 112   2. In the subtraction of two numbers in base two, the following rules applied:     02 – 02 = 02   12 – 02 = 12 … Read more

(E) Converting from One Base to Another 1. The following steps are used to convert a number from one base to another base. (a) convert the number to a number in base 10 by using expended notation. (b) use repeated division to convert the number in base 10 to the respective bases. Example 1: Convert (a) 1101012 … Read more

(D) Converting Numbers in Base Two, Eight and Five to Base Ten and Vice Versa 1. Steps to convert numbers in base 2, 8 and 5 to base 10 are as follows. (a) write the number in expanded notation. (b) simplify the expanded notation into a single number.   Example 1: Convert each of the following … Read more

(A) Numbers in Bases Two, Eight and Five 1. The numbers we use daily are in base ten. The ten digits used in numbers in based ten are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. 2. Numbers in base two are numbers that use two digits only. The digits are 0 and 1. Example: 1011012. 3. Numbers in … Read more