Lesson 2, Topic 3
In Progress

# Conversion from one Base to Another

Lesson Progress
0% Complete

#### Topic Content:

• Conversion from one Base to Another

It is important to know that a number given in one base other than base ten can be converted to another base via base ten.

### Example 2.3.1:

Evaluate the following and express the answer on the bases indicated.

(i) 10401.117 to base eight
(ii) 2013 – 101012 + 2536 to base 6

(i) Convert 10401.117 to base ten

Solution:

i.e $$\scriptsize 10401.11_7 \\ \scriptsize = 1 \: \times \: 7^4 \: + \: 0 \: \times \: 7^3 \: + \: 4 \: \times \: 7^2 \\ \scriptsize \:+\: 0 \: \times \: 7^1 \: + \: 1 \: \times \: 7^0 \: + \: 1 \: \times \: 7^{-1} \: + \: 1 \: \times \: 7^{-2}$$

= $$\scriptsize 20141 \: + \: 0 \: + \: 196 \: + \: 0 \: + \: 1 \: + \: 0.142 \: + \: 0.0204$$

= $$\scriptsize 2598.1624$$

Convert to base 8

Whole number part

Decimal part

i.e. $$\scriptsize 0.1624_8 = 0.123_8$$

Aswer: $$\scriptsize 10401.11_7 = 5046.123_{8}$$

(ii) 2013 – 101012 + 2536 to base 6

Solution:

Convert all numbers to base ten

$$\scriptsize 201_3 \\ \scriptsize = 2 \: \times \: 3^2 \: + \: 0 \: \times \: 3^1 \: + \: 1 \: \times \: 3^0 \\ \scriptsize = 18 \: + \: 0 \: + \: 1 \\ \scriptsize = 19$$

$$\scriptsize 10101_2 \\ \scriptsize = (1 \: \times \: 2^4 )\: + \: (0 \: \times \: 2^3) \: + \: (1 \: \times \: 2^2) \\ \scriptsize \: + \: (0 \: \times \: 2^1) \: + \: (1 \: \times \: 2^0) \\ \scriptsize = 16 \: + \: 0 \: + \: 4 \: + \: 0 \: + \: 1 \\ \scriptsize = 21$$

$$\scriptsize 253_6 \\ \scriptsize = 2 \: \times \: 6^2 \: + \: 5 \: \times \: 6^1 \: + \: 3 \: \times \: 6^0 \\ \scriptsize = 72 \: + \: 30 \: + \: 3 \\ \scriptsize = 105$$

i.e $$\scriptsize 201_3 \: – \: 10101_2 \: + \: 253_6 \\ \scriptsize = 19 \: – \: 21 \: + \: 105 \\ \scriptsize = 124 \: – \: 21 \\ \scriptsize = 103$$

Answer: $$\scriptsize 201_3 \: – \: 10101_2 \: + \: 253_6 = 251_6$$

### Example 2.3.2:

Find the value of x in the following:

(i) $$\scriptsize 315_x \: -\: 223_x = 72_x$$
(ii) $$\scriptsize (251.25)_{10} = x_7$$

(i) $$\scriptsize 315_x \: -\: 223_x = 72_x$$

Solution:

You are viewing an excerpt of this Topic. Subscribe Now to get Full Access to ALL this Subject's Topics and Quizzes for this Term!

Click on the button "Subscribe Now" below for Full Access!

### Subscribe Now

Note: If you have Already Subscribed and you are seeing this message, it means you are logged out. Please Log In using the Login Button Below to Carry on Studying!