1. Mathematics with Binary

2. Question  Below is a binary string  Which is the least significant bit (LSB)?  Which is the most significant bit (MSB)? 0 0 0 1 0 1 1 1 MSBLSB

3. Objectives  Add two binary numbers and multiply two binary numbers.  Convert a denary integer into Two's Complement and vice versa.  Describe the use of Two's Complement to perform subtraction.

4. Binary Addition  You have to be able to add together two binary numbers, and it’s easy!  Lets try to add together  00011001  00011010 00011001 00011010 1 1 0 0 1 1 1 1 0 0

5. Binary Subtraction  Subtraction has an extra step as we have to use two’s complement, to make the number that we are taking way into a negative  Two’s Complement is used to convert a number to a negative  Lets look at taking away the following:  00010001 (17)  00001101 (13 – Decimal) Step 1 – Convert 13 to twos complement 11110011 Step 2 – We now add together the two numbers 11110011 00010001 0 0 1 0 0 00 0 11 1 1 1 1

6. Binary Multiplication  This can be slightly longer but follows the same rules as doing multiplication in denary.  Lets look at multiplying the following numbers:  10110  00101 10110 00101 10110..... 1101110 1