GCSE Computing: A451 Computer Systems & Programming Numbers Representation of Data in Computer Systems

GCSE Computing: A451 Computer Systems & Programming Activity 1 5 minutes to complete the following: Convert the following binary numbers into denary

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Introduction Last lesson we looked at the binary number system and the need for data to be converted into binary so that it can be processed by the CPU. Today we will look at how NUMBERS are represented in binary… Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers.

GCSE Computing: A451 Computer Systems & Programming Representing Numbers

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Converting Binary Numbers In your exam you will be expected to be able to convert a denary number (the numbers humans work with (base 10) into binary… …and back again Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers.

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Converting from Binary to Denary (easy) If you are given a binary number which is to be converted into denary do the following: 1.Above each bit, write the value of that bit. 2.Then simply add the values where there is a 1 underneath, together Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers.

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Converting from Binary to Denary (easy) Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers.

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Converting from Denary to Binary Converting from denary to binary is also quite straight forward. If we wanted to convert 202 into binary we would do the following: Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers. Does 128 fit into 202? YES! So we add a 1 into the column and subtract 128 from 202 (leaving 74) 1

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Converting from Denary to Binary Converting from denary to binary is also quite straight forward. If we wanted to convert 202 into binary we would do the following: Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers. Does 64 fit into 74? YES! So we add a 1 into the column and subtract 64 from 74 (leaving 10) 1 1

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Converting from Denary to Binary Converting from denary to binary is also quite straight forward. If we wanted to convert 202 into binary we would do the following: Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers. Does 32 fit into 10? NO! So we add a 0 into the column and move on… 1 1 0

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Converting from Denary to Binary Converting from denary to binary is also quite straight forward. If we wanted to convert 202 into binary we would do the following: Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers. Does 16 fit into 10? NO! So we add a 0 into the column and move on…

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Converting from Denary to Binary Converting from denary to binary is also quite straight forward. If we wanted to convert 202 into binary we would do the following: Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers. Does 8 fit into 10? YES! So we add a 1 into the column and subtract 8 from 10 (leaving 2)

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Converting from Denary to Binary Converting from denary to binary is also quite straight forward. If we wanted to convert 202 into binary we would do the following: Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers. Does 4 fit into 2? NO! So we add a 0 into the column and move on…

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Converting from Denary to Binary Converting from denary to binary is also quite straight forward. If we wanted to convert 202 into binary we would do the following: Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers. Does 2 fit into 2? YES! So we add a 1 into the column and subtract 2 from 2 (leaving 0)

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Converting from Denary to Binary Converting from denary to binary is also quite straight forward. If we wanted to convert 202 into binary we would do the following: Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers. Does 1 fit into 0? NO! So we add a 0 into the column and that is it!

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Converting from Denary to Binary So 202 in binary is: Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers Check that it works:

GCSE Computing: A451 Computer Systems & Programming Mini Whiteboard Practice Convert 234 into binary:

GCSE Computing: A451 Computer Systems & Programming Mini Whiteboard Practice Convert 42 into binary:

GCSE Computing: A451 Computer Systems & Programming Mini Whiteboard Practice Convert 175 into binary:

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Adding 8-bit binary numbers Adding binary numbers is much like adding denary numbers (the system we use as humans). Things to remember: 1.Keep your numbers in the correct columns = 10 in binary = 11 in binary Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers.

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Adding 8-bit binary numbers Adding binary numbers is much like adding denary numbers (the system we use as humans). Things to remember: 1.Keep your numbers in the correct columns = 10 in binary = 11 in binary Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers.

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Adding 8-bit binary numbers Adding binary numbers is much like adding denary numbers (the system we use as humans). Things to remember: 1.Keep your numbers in the correct columns = 10 in binary = 11 in binary Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers.

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Adding 8-bit binary numbers Adding binary numbers is much like adding denary numbers (the system we use as humans). Things to remember: 1.Keep your numbers in the correct columns = 10 in binary = 11 in binary Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers.

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Adding 8-bit binary numbers Adding binary numbers is much like adding denary numbers (the system we use as humans). Things to remember: 1.Keep your numbers in the correct columns = 10 in binary = 11 in binary Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers.

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Adding 8-bit binary numbers Adding binary numbers is much like adding denary numbers (the system we use as humans). Things to remember: 1.Keep your numbers in the correct columns = 10 in binary = 11 in binary Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers.

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Adding 8-bit binary numbers Adding binary numbers is much like adding denary numbers (the system we use as humans). Things to remember: 1.Keep your numbers in the correct columns = 10 in binary = 11 in binary Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers.

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Adding 8-bit binary numbers Adding binary numbers is much like adding denary numbers (the system we use as humans). Things to remember: 1.Keep your numbers in the correct columns = 10 in binary = 11 in binary Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers.

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Adding 8-bit binary numbers Adding binary numbers is much like adding denary numbers (the system we use as humans). Things to remember: 1.Keep your numbers in the correct columns = 10 in binary = 11 in binary Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers.

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems Adding 8-bit binary numbers A quick check… Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers = = 194

GCSE Computing: A451 Computer Systems & Programming Mini Whiteboard Practice Add the following 2 binary numbers:

GCSE Computing: A451 Computer Systems & Programming Mini Whiteboard Practice Add the following 2 binary numbers:

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems What about the following situation Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers. 1 0 If the last part of the addition means that there is a carry, we simply place it as the first number. This will mean that the answer is a 9-bit answer.

GCSE Computing: A451 Computer Systems & Programming Representation of Data in Computer Systems The problem with 9-bit answers Because the largest number we can hold in a byte is 255, if we add two bytes together there is a chance that the answer will be greater than 255. This answer will not be able to be held in a byte and so this causes an over flow error. In modern computers, CPU’s can hold much larger numbers so this is dealt with. Ever heard of a 32 or 64 bit processor? – these can deal with larger binary numbers! However you do need to know that overflow errors occur when doing binary addition when the answer is 9 bits in length. Learning Objectives: Numbers: a)Convert positive denary numbers (0-255) into 8- bit binary numbers and vice versa. b)Add two 8-bit binary integers and explain overflow errors which may occur c)Convert positive denary whole numbers (0-255) into 2-digit hexadecimal number and vice versa d)Convert between denary and hexadecimal equivalents of the same number e)Explain the use of hexadecimal to represent binary numbers. = OVERFLOW ERROR!

GCSE Computing: A451 Computer Systems & Programming Mini Whiteboard Practice Add the following 2 binary numbers:

GCSE Computing: A451 Computer Systems & Programming Mini Whiteboard Practice Add the following 2 binary numbers: