Back to Course

SS1: MATHEMATICS - 1ST TERM

0% Complete
0/0 Steps
  1. Number Base System I | Week 1
    6 Topics
    |
    2 Quizzes
  2. Number Base System II | Week 2
    3 Topics
  3. Number Base System III | Week 3
    2 Topics
    |
    1 Quiz
  4. Modular Arithmetic I | Week 4
    2 Topics
  5. Modular Arithmetic II | Week 5
    3 Topics
  6. Modular Arithmetic III | Week 6
    4 Topics
    |
    1 Quiz
  7. Indices I | Week 7
    3 Topics
    |
    1 Quiz
  8. Indices II | Week 8
    1 Topic
    |
    1 Quiz
  9. Logarithms I | Week 9
    3 Topics
  10. Logarithms II | Week 10
    4 Topics
    |
    1 Quiz



Lesson Progress
0% Complete

Topic Content:

  • Addition in Other Bases

When adding binary numbers some simple rules can be used.

The rules of binary addition are:

  • 0 + 0 = 0
  • 0 + 1 = 1
  • 1 + 0 = 1
  • 1 + 1 = 0 with a Carry of 1
  • 1 + 1 + 1 = 1 with a Carry of 1

But we can also use another technique for the addition of binary and other bases, as shown below.

Example 1.4.1:

Evaluate the following:

1. 111100two + 10111two + 10011two
2. 110.011two + 10.111two + 1.01two 
3. 13047 + 467 + 1426
4. 5D6C16 + 6ABF16 + 3D216

1. 111100two + 10111two + 10011two

Solution

Screenshot 2023 09 13 at 15.45.03

Explanation

1st Column (from right to left): 0 + 1 + 1 = 2. How many twos are there in 2? The answer is 1 remainder 0. Write 0 and carry 1 to column 2.

2nd Column: 1 + 0 + 1 + 1 = 3. How many twos are there in 3? The answer is 1 remainder 1. Write 1 and carry 1 to column 3.

3rd Column: 1 + 1 + 1 + 0 = 3. How many twos are there in 3? The answer is 1 remainder 1. Write 1 and carry 1 to column 4.

4th Column: 1 + 1 + 0 + 0 = 2. How many twos are there in 2? The answer is 1 remainder 0. Write 0 and carry 1 to column 5.

5th Column: 1 + 1 + 1 + 1 = 4. How many twos are there in 4? The answer is 2 remainder 0. Write 0 and carry 2 to column 6.

6th Column: 2 + 1 = 3. How many twos are there in 3? The answer is 1 remainder 1. Write 1 and carry 1 to the next (7th)column.

This yields 1100110two

2. 110.011two + 10.111two + 1.01two 

 

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!

avatar

Responses

Your email address will not be published. Required fields are marked *

error: Alert: Content selection is disabled!!