2. Numbers (Data Conversion)

Numbers: Denary to Binary

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

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

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 = + + +  = 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.

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:

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:

Binary Addition and Overflow

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 denary 

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 shifts Student Worksheet

Binary numbers can be shifted  left or right

• A single left shift doubles the number
• A single right shift halves the number

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 =

c) Which shift can be used to double the value of the binary number 00100100.

Answer:  A single shift