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The binary number system has two unique values: a 0 and 1. This number system and primarily used by computers
The denary(decimal), there are ten unique numbers (0-9). This is our everyday number system.
Q1a)If binary is a base 2 number system, what do you think denary would be?
Answer:Â Base Fill in the blank 1 of 28
Q1a)How many bits in a byte?
Answer:Â Fill in the blank 2 of 28
Converting between binary and denary.Â
We can use a byte table to perform conversions. As shown below, its a good to remember this pattern
Q2) What you notice about the above pattern?
Answer:Â All numbers Fill in the blank 3 of 28
RULE: When performing binary conversions you always work right to left
If we convert 01010001 to denary we quite simply complete the table right to left
Then we add the denary values up
01010001 = = 64+16+1 = 81
Have a go at converting the following
Q3a) Convert 01010011 into denary by completing the below table
Q3b) Then the denary value together
Answer = Fill in the blank 12 of 28 + Fill in the blank 13 of 28 + Fill in the blank 14 of 28 +Â Fill in the blank 15 of 28 = 83
Q4) Convert 11010011 into denary
Answer:Â Fill in the blank 16 of 28
We can use a similar method to convert denary to binary. Lets convert the denary value 131 into binary.
Again we can use the byte table and see which values we require to make 131 and place a binary 1 in under the column.
Therefore, the binary number for 131 is 10000011
Q5) Convert denary 88 into a binary number by completing the below table
Q6) Convert denary 255 into a binary number
Answer: Fill in the blank 25 of 28
Q7) Convert denary 192 into a binary number
Answer: Fill in the blank 26 of 28
Q8) Convert denary 174 into a binary number
Answer:Â Fill in the blank 27 of 28
Q9) What is the term used when the denary value exceeds 255?
Answer: Fill in the blank 28 of 28
There are four rules that need to be followed when adding two binary numbers. These are:
0 + 0 = 0 1 + 0 = 1 1 + 1 = 10 (binary for denary 2) 1 + 1 + 1 = 11 (binary for denary 3)
Check the answer by converting this to denaryÂ
81 + 173 = 234
Q1) Use the following table to add the following binary numbers together:
Binary Overflow
8-bit binary has a maximum value of 11111111 (255)
Anything over this value, for example 278, will produce an overflow error.
10110111 = 183
11110110 = 246
Total   = 429
Any value that is over 255 should be expressed as Binary number = 00000000
Binary numbers can be shifted left or right
Binary numbers can be shifted right multiple places.
Exam Question
a) Show the effect of a binary shift right of two places on the binary number 00110100.
b) To perform the denary check, how many do you divide 52 by?
Answer = Fill in the blank 13 of 14
c) Which shift can be used to double the value of the binary number 00100100.
Answer:Â A single Fill in the blank 14 of 14 shift
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