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Each word must spelled correctly. Answers are not case sensitive.
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: Base
Q1a)How many bits in a byte?
Answer:
Converting between binary and denary.
We can use a byte table to perform conversions. As shown below, its a good to remember this pattern
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Q2) What you notice about the above pattern?
Answer: All numbers
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
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
Then we add the denary values up
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | = 64+16+1 = 81 |
| 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
01010001 = = 64+16+1 = 81
Have a go at converting the following
Q3a) Convert 01010011 into denary by completing the below table
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Q3b) Then the denary value together
Answer = + + + = 83
Q4) Convert 11010011 into denary
Answer:
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.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
Therefore, the binary number for 131 is 10000011
Q5) Convert denary 88 into a binary number by completing the below table
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 |
Q6) Convert denary 255 into a binary number
Answer:
Q7) Convert denary 192 into a binary number
Answer:
Q8) Convert denary 174 into a binary number
Answer:
Q9) What is the term used when the denary value exceeds 255?
Answer:
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)
| Binary Number 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
| Binary Number 2 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
| Carry | 1 |
| Answer | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
Check the answer by converting this to denary
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | = 64+16+1 = 81 |
| 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 |
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | = 128+32+8+4+1 =173 |
| 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
81 + 173 = 234
Q1) Use the following table to add the following binary numbers together:
| Binary Number 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 |
| Binary Number 2 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
| Carry | ||||||||
| Total |
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
Each word must spelled correctly. Answers are not case sensitive.
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.
| 128 | 64 | 32 | 16 | 8 | 4 | 2 | 1 | SHIFT RIGHT 1 | SHIFT RIGHT 2 | Denary Check |
| 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | |||
b) To perform the denary check, how many do you divide 52 by?
Answer =
c) Which shift can be used to double the value of the binary number 00100100.
Answer: A single shift
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