a)Convert positive denary whole 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 numbers and vice versa. d)Convert between binary and Hex equivalents of the same number e)Explain the use of Hex numbers to represent binary numbers Candidates should be able to:

Have a go at converting denary to binary numbers on the booklet provided OR Binary Nibble Bingo Starter

 FEW RULES: Adding binary numbers together

Adding binary numbers together

Step 1: Start off by putting the numbers in the top 2 rows in a 4 row table. 3 rd row will hold any carry overs 4 th row will contain the answer Adding binary numbers together

Step 2: Add the column on the right together From the rules above we know that 1+1 = 10 Adding binary numbers together

Step 2: Put a 0 on the bottom row & we carry a 1 over into column 7 Adding binary numbers together

Step 3: Column 7 Add the 3 rows together = 10 Adding binary numbers together

Step 3: Column 7 Put 0 at bottom of column 7 Carry the 1 to row 3 of column 6 Adding binary numbers together

Step 4: Column = 10 Adding binary numbers together

Step 4: Column 6 Put 0 down Carry 1 over to column 5 Adding binary numbers together

Step 5: Column = 11 Adding binary numbers together

Step 5: Column 5 Put 1 down in column 5 Carry 1 over to row 3 column 4 Adding binary numbers together

Step 6: Column = 11 Adding binary numbers together

Step 6: Column 4 Put 1 down in column 4 Carry 1 over into column 3 Adding binary numbers together

Step 7: Column Adding binary numbers together

Step 7: Column 3 Put 1 down in column 3 row 4 Carry 0 to column 2 Adding binary numbers together

Step 8: Column =0 Adding binary numbers together

Step 8: Column 2 Put 0 down in column 2 row 4 Carry 0 into column 1 row 3 Adding binary numbers together

Step 9: Column = 1 Adding binary numbers together

Step 9: Column 1 Put 1 down in column 1 row 4 Nothing to carry over Adding binary numbers together

RESULTS: Adding binary numbers together

 The last binary add was straightforward. HOWEVER what would happen if the sum in column 1 had been 1+1?  The carried 1 would have nowhere to go and would be lost.  The problem is called overflow and causes the wrong answer. Overflow Errors

 To “solve” this problem what normally happens is a flag in the CPU (processor)  The software that has caused the error MUST check to see if this flag has been set - & if so it has to handle the problem. Overflow Errors

nversion.html