Data Representation AS

​Binary Digits

• ​By the end of the lesson you must be able to :

  1. Change binary digits to decimals

  2. Add or subtract binary digits

  3. Use the 1's and 2's compliment

  4. Express numbers in BCD
     

Multiple Choice

Numbers in base 10 system are called denary numbers or traditionally called ____

• powers of 2

• bytes

• hexadecimals

• decimals

Multiple Choice

A digit in the binary number system written using either of the symbols 0 and 1 is called a

• denary

• bit

• byte

• nibble

Multiple Choice

A group of four bits is a nibble , what of a group of eight bits treated as a single unit

• byte

• bit

• nibble

• decimal

Multiple Choice

What is 162 in hexadecimal form ?

• 2A

• 0

• 1A

• A2

Fill in the Blank

Change 3E into denary form

Fill in the Blank

Write 89 in an 8 bit binary form

Multiple Choice

1000 bytes =

• 1kilobyte(1kb)

• 1 kibibyte(1kib)

• 1mb

• 1 mib

Multiple Choice

A prefix to define the magnitude of a value. Examples are kibi, mebi, gibi and tebi

representing factors of 2¹⁰, 2²⁰, 2³⁰ and 2⁴⁰ respectively is called ___

• Binary prefix:

• decimal prefix

• hexadecimal prefix

• byte prefix

Fill in the Blank

Look at this number , what is it in denary form

Fill in the Blank

Add these bianry numbers .

​Adding binary digits

​We added 7 bit digits and ended up with an 8 bit answer . We call this an Overflow error

Multiple Choice

A condition when the result of a calculation is too large to fit into the number of bits defined for storage

• a logical shift

• an overflow

• a syntax error

• a logical error

Fill in the Blank

Add these 5 bit binary digits 10111 + 00101

​This is an 8 bit binary digit it represents 64+ 16+8+1 = 89.

​ 1 1 1 1 1 1 1 1

​

​

​When we have all ones throughout we will have a total of 128+64+32+16+8+4+2+1=

Fill in the Blank

​When we have all ones throughout we will have a total of 128+64+32+16+8+4+2+1=

​This is an 8 bit binary digit it represents 64+ 16+8+1 = 89.

​ 1 1 1 1 1 1 1 1

​

​When we have all ones throughout we will have a total of 128+64+32+16+8+4+2+1= 255
This shows the maximum value an 8 bit digit can store

​When we have all ones throughout we will have a total of 128+64+32+16+8+4+2+1= 255
This shows the maximum value an 8 bit digit can store

We can obtain this 255 by saying 2⁸-1 = 2X2X2X2X2X2X2X2-1= 255

This means for a 16 bit binary digit the maximum value we can store is
2¹⁶-1=65536-1= 65535.

32768+16384+8192+4096+2048+1024+512+256+128+64+32+16+8+4+2+1

Fill in the Blank

What is the maximum denary value that can be stored by a 6 bit binary digit.

The two's compliment
Helps to represent intergers in binary form

​This means the range of the digits changes since the last bit becomes signed.

Multiple Choice

Can we write negative numbers numbers in binary form

• Yes

• No

Multiple Choice

What determines whether the number is positive or negative when we decide to write numbers in two's compliment ?

• The number of bits

• When we convert the number to decimal

• The left most digit whether it's a 0 or 1

Multiple Choice

If the left most digit is 1 it means the number is

• a negative integer

• A positive integer

• out of the range

​The one's compliment

Watch the Gif above . Write on a piece of paper what you are seeing happening .

Fill in the Blank

This is flipping of numbers. Flipping the binary digits is known as 1's compliment.

Can you write one's compliment of the binary digit

00101001

Multiple Choice

The one’s complement of a binary number, plus 1 is called -

• one's compliment

• two's compliment

• signed number

• left most digit

Fill in the Blank

What is the one's compliment of 00010001

​What we have is a two's compliment now.

​

​It is a representation of the number -128+32+4+2 +1 = -89

Multiple Choice

This is a signed 8 bit binary digit . What is the value in denary of 10011100 in denary ? REMEMBER THE LEFT MOST DIGIT DETERMINES WHETHER IT IS A POSITIVE OR NEGATIVE INTEGER IN ALL SIGNED BINARY DIGITS.

• -28

• 100

• 28

• -100

Fill in the Blank

Write the 8 bit binary digit 01100110 in two's compliment

Fill in the Blank

-20 may be signed and written as a binary digit . Write it as an 8 bit binary digit.

​Lets have a look at Bonary coded digits

They are all nibbles(4bits)
Check their denary equivalent

​Example
14 = 00010100
20= 00100000
Check the value of nibbles

Multiple Choice

Write the BCD 1000 0101 in Denary form

• 81

• 85

• 133

• 1111