Binary numbers

Learning objectives & evaluation criteria -Represent positive decimal numbers in binary -Perform addition and multiplication on binary numbers using the twos complement system -Know how to convert decimal number to binary -Can convert negative decimal number to binary -Describe all steps convert decimal to binary

-How can we represent decimal numbers in binary notation? -What are the arithmetic operations we can perform on binary numbers?

The process of performing addition in binary is very similar to addition in decimal. There are four simple rules: Binary Addition Rules: = = = 0 carry = 1 carry The total number is bigger than 5 bits (the space allocated to it); this is called an overflow because the computer has nowhere to store it. This is known as an overflow error. © ZigZag Education, 2015

Subtraction Twos complement can help with binary subtraction. First we convert the second number to its negative equivalent in twos complement Next we add the numbers together using the rules of binary addition. If there is an overflow it is discarded. We do this by reversing the bits and adding 1 to the number. © ZigZag Education, 2015

Binary multiplication is a simple process. Follow these steps: Binary Multiplication × Write the first number underneath the second number in line with each 1. Next add the numbers together using the binary addition rules © ZigZag Education, 2015

Here are some more examples: Binary Multiplication × × For the last example we used a new rule: = 0 carry 0 and carry 1 to the next column. This is because produces 4 which is 100 in binary. © ZigZag Education, 2015

Practise work 1 Convert the following decimal number to binary number system To check you answers please use Harvards website 15= 3= 47= 65= 79= 123=

Practise work = = = = 11 * 11= 1011 * 101= 1111 * 111= = = – 110= – 1100= – 1011= Run the self test using the Calculator.

Разминка - Количество цифр в двоичной системе счисления сложить с количеством бит в одном байте. - Результат умножить на десятичное число, которое в двоичной системе счисления записывается: К полученному результату прибавить отличную школьную оценку. -Ответ перевести в двоичную систему счисления и представить жюри. -Ответ

Research work Ok we know how to convert decimal to binary. But if we have negative decimal number, How will we convert to binary??? For solution of this problem i will give link which shows how to convert. goo.gl/EWR5uo

Practise work 3 Convert negative decimal to binary: = = -57= -71=

Formative assessment

Reflection