Chapter 1 : Number Bases

Numbers in Base Two, Eight, and Five*Stating numbers in base two,eight and five

(a) Numbers in :

Base two use only two digits , 0 , 1.

Base eight use only eight digits,1,2,3,4,5,6 and 7.

Base five use only five digits 0,1,2,3 and 4.

(b) Zero ,one, two, three, ... in base two , eight and five  are written as follows .

*Place value of a digit of a number in base two,eight and five are given in the table below.

a) The value of a digit of a number in base two,eight or five is determined as follows.

          

*Writing numbers in base two, eight and five in expanded notation 

Chapter 1 : Number Bases

A number in base two,eight or five can be written in expanded notation according to the corresponding place value of each digit.

The 351710 in base ten can be written in expanded notation in the form of 3 x 10³ + 5 x 10² + 1 x 10¹ + 7 10 x 10°.

*Converting numbers in base two,eight and five to numbers in base ten and vice versa

(a) To convert a number in base two,eight  or five to a number in base ten :Write the number in expanded notation .

Find the sum of the value of all the digits.

(b) To convert a number in base ten to a number in base two,eight or five,follow the steps below :Divide the number repeatedly by 2, 8 or 5,until the quotient is 0.

Write the remainders from the bottom to the top.

Chapter 1 : Number Bases

*Converting numbers in a certain base to numbers in another base

( I ) Base two to base eight      To convert a number in base two to base eight :

Method 1

Method 2Group the digits into group of three,starting from the right end.

Substitute each group by an equivalent digit in base eight..

( II ) Base eight to base two       To convert  a number in base eight to base two :Method 1

Method 2 Substitute each digit by three corresponding digits in base two.

( III ) Base two or eight to base five        To convert a number from base two or base eight to base five,we have to convert the number to base ten first. 

Chapter 1 : Number Bases

( IV ) Base five to base two or eight        To convert  a number from base five to base two or base eight,we have to convert the number to base ten.

*Addition and subtraction of two numbers in base twoComputations involving addition and subtraction of numbers in base two can be done in the same manner as computations in base ten.