Binary Addition, Study Guides, Projects, Research of Mathematics

By the end of this worksheet you should: • know how a computer adds two binary values together. • be able to define what is meant by a carry.

Typology: Study Guides, Projects, Research

2021/2022

Uploaded on 09/12/2022

mdbovary
mdbovary 🇬🇧

4.8

(8)

215 documents

1 / 4

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Page%1%of%4%
Binary'Addition'
%
By%the%end%of%this%worksheet%you%should:%
%
know%how%a%computer%adds%two%binary%
values%together%
be%able%to%define%what%is%meant%by%a%carry%
%
%
Computers%can’t%do%much;%but%they%do%it%incredibly%
quickly.%
%
One%things%computers%can%do%is%add.%
%
Yet%computers%use%binary,%so%we%need%to%know%how%
computers%add%two%binary%numbers%together.%
%
%
%
BINARY:%% A%numbering%system%used%by%computers%and%
digital%circuits.%
Uses%2%values;%0%or%1.%
%
DENARY:% A%numbering%system%used%by%humans%around%
the%world.%
Uses%10%values:%0,%1,%2,%3,%4,%5,%6,%7,%8%or%9.%
%
%
%
Why?%Why%do%we%need%to%know%how%to%add%two%binary%
numbers%together?%
%
Well,%it’s%not%to%check%that%you%can%add%two%1s%together;%
we’re%sure%you%can%do%that.%
%
It’s%because%knowing%how%your%computer%works%is%key%to%
understanding%programming%and%how%computers%do%the%
things%they%do.%
%
Now,%it%is%important%to%remember%the%following:%
%
% 0%+%0%=%0%
% 0%+%1%=%1%
% 1%+%0%=%1%
% 1%+%1%=%2%
% 1%+%1%+%1%=%3%
pf3
pf4

Partial preview of the text

Download Binary Addition and more Study Guides, Projects, Research Mathematics in PDF only on Docsity!

By the end of this worksheet you should:

  • know how a computer adds two binary values together
  • be able to define what is meant by a carry Computers can’t do much; but they do it incredibly quickly. One things computers can do is add. Yet computers use binary, so we need to know how computers add two binary numbers together. BINARY : A numbering system used by computers and digital circuits. Uses 2 values; 0 or 1. DENARY : A numbering system used by humans around the world. Uses 10 values: 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9. Why? Why do we need to know how to add two binary numbers together? Well, it’s not to check that you can add two 1s together; we’re sure you can do that. It’s because knowing how your computer works is key to understanding programming and how computers do the things they do. Now, it is important to remember the following: 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 2 1 + 1 + 1 = 3

Again, this is obvious but we also know that computers only use binary (zeros and ones), so there is no 2 or 3. Instead, we need to use the binary equivalent values for 2 and 3, which are: 0 00 1 01 2 10 3 11 And then we need to remember the old carry we do in our own mathematics. Carry? Consider adding these two denary values together: 2 5 1 1 7 5 4 2 6 1 Look at the small 1 at the bottom of the last column; that is a carry. This is there because when we add 5 and 7 together we get a value bigger than 9; so, we need to carry the tens part of the answer into the next column. CARRY : to transfer to the next column. In maths, if the result of a calculation exceeds the maximum value for that column, the additional amount is ‘carried over’ to the next, more significant, column. We do the same in binary: (^0 1 0 1 1 0 0 ) (^0 0 1 1 0 1 0 ) 1 0 0 0 1 1 1 0 1 1 1 1

Try these… a) 0 1 0 1 1 0 0 1 0 1 1 0 0 1 0 0 b) 0 0 0 1 1 0 0 1 1 0 1 0 1 0 1 1 c) 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 d) 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 e) 0 1 0 1 1 0 0 1 0 1 1 0 0 0 0 0 f) 1 0 1 0 1 0 1 1 0 0 0 1 0 1 0 1