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**Candidates should be able to:**

Convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa Add two 8-bit binary integers and explain overflow errors which may occur Convert positive denary whole numbers (0-255) into 2-digit hexadecimal numbers and vice versa. Convert between binary and Hex equivalents of the same number Explain the use of Hex numbers to represent binary numbers

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Hexadecimal Numbers Hexadecimal is the name given to numbers using base 16 Decimal numbers 10 – 15 are represented using letter A – F 16 values so base 16

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Hexadecimal Used in computing as it is a much shorter way of representing a byte of data. Binary data = 8 digits, Hexadecimal data = 2 digits E.G = FF Largest byte value is 255 and hexadecimal can represent up to that number

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Binary to Hexadecimal HEX is used to express binary numbers in a more compact form HEX numbers run from Zero to F (15 decimal) 15 decimal = 1111 (nibble) = F (Hex)

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**11011110 = DE (Hex) Binary to Hexadecimal**

Example 1 – as Hex number Split number into 2 nibbles (1101…..1110) Convert number to decimal 1101 = 13 1110 = 14 Convert number to Hex 13 = D 14 = E = DE (Hex)

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**1110 0011 (E3 in binary) Hexadecimal to Binary**

Example 1 – E3 as binary number Take 1st Hex digit – convert to binary nibble 3 Hex = 3 decimal = 0011 binary Take 2nd hex digit – convert to binary nibble E Hex = 15 decimal = 1110 binary Put the 2 nibbles together (E3 in binary)

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**Decimal to Hexadecimal conversion**

Example 1 – 55 as Hex number Put headings etc Write out binary number (55) Split into 2 nibbles: 0011…0111 0011 = 3 0111 = 7 55 = 37 (Hex)

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**Decimal to Hexadecimal conversion**

Example 2 – 17 as Hex number Put headings etc Write out binary number (17) Split into 2 nibbles: 0001…0001 0001 = 1 17 = 11 (Hex)

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**Have a go at these OR – MUCH HARDER**

OR – MUCH HARDER

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Have a go at the Test

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Binary Aim: Explain binary and binary units Objective 1: Convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa Objective.

Binary Aim: Explain binary and binary units Objective 1: Convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa Objective.

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