1.1 Binary Hex Number Systems + Text Flashcards
Why do computers use binary to represent all forms of data?
- Any form of data needs to be converted to binary to be processed by a computer
- Data is processed using logic gates and stored in registers
Explain the concept of overflow and why it occurs in binary addition
- A computer or a device has a predefined limit that it can represent or store e.g. 16-bits
- Overflow errors happen when the largest number that a CPU register can hold is exceeded.
- The number of bits that a CPU can handle is called the word size.
- When adding 2 binary numbers an overflow error occurs when a value outside this limit is stored e.g if the value is greater than 255 in an 8-bit register
Explain the difference between the binary and denary number systems
- Binary base 2 system
- Denary base 10 system
- Binary has 2 digits (0 and 1)
- Denary has 10 digits (0-9)
- Binary place values are powers of 2
- Denary place values are powers of 10
What are the binary place values for a byte?
128 64 32 16 8 4 2 1
Convert the binary number 10011011 into denary
155
Convert the denary value 156 into binary
10011100
What is the largest value that can be stored in 8 bits?
255
What is the largest value that can be stored in 10 bits?
1023
What would be the effect of shifting the bits 1 place to the left for the binary value 0001 1101
- Multiplying by 2
- 0001 1101 = 29
- 00111010 = 58
What would be the effect of shifting bits 3 places to the left?
- multiply by 8 or multiply by 2 x 2 x 2 or multiply by 2^3
- 0000 0110 = 6
- 0011 0000 = 48
What would be the effect of shifting bits 2 places to the right?
- divide by 4 or divide by 2^2
- 0001 0000 = 16
- 0000 0100 = 4
How many bits in a byte?
8
How many bits in a nibble?
4
How many nibbles in 4 bytes?
8
What is a register?
- A register is a small amount of internal memory
- Used for fast reading and writing
- It is temporary/volatile (loses data once there is no power)
What are the rules you need to remmeber for binary addition?
- 0 + 1 = 1
- 1+ 1 = 2 = 0 Carry 1
- 1+1+1 = 3 = 1 Carry 1
Add the 2 binary values 00100111 + 01001010
01110001
Add the 2 binary values 01110010 + 11111001. If you tried to store the result in word size of 8 bits what error would occur?
Requires 9 bits (101101011) so overflow error
What are the binary place values for a 2’s Complement byte?
-128 64 32 16 8 4 2 1
What is the smallest value that can be stored in a 2’s Complement byte?
- -128 64 32 16 8 4 2 1
- 1 0 0 0 0 0 0 0= -128
What is the largest value that can be stored in a 2’s Complement byte?
- -128 64 32 16 8 4 2 1
- 0 1 1 1 1 1 1 1 = 127
Negative denary numbers can be represented as binary using ….
2’s Complement
Convert the 2’s Complement binary number below to denary
11111111
-1
Convert the 2’s Complement binary number below to denary
10001000
-120
Convert the denary number below to 2’s Complement binary
-19
11101101
Convert the denary number below to 2’s Complement binary
-7
11111001
What is hexadecimal?
- Base 16 number system
- 16 choices of digits (0-9, A-F)
- Place values are powers of 16
What are the place values for the hexadecimal value A7F3?
- 4096 256 16 1
- A 7 F 3
What is the denary value of the hex digit A?
10
What is the denary value of the hex digit E?
14
What is the denary value of the hex digit 7?
7
Convert the hex value AAA to Denary
2730
Convert the following hex values to denary
- 1F
- 42
- CC
- 1F = 31
- 42 = 66
- CC = 204
Convert the hex value CA to Binary
11001010
Convert the following hexadecimal values to binary
- B3
- 5A
- B0F
- B3 = 1011 0011
- 5A = 0101 1010
- B0F = 1011 0000 1111
Convert the binary value 1111 1010 to hexadecimal
FA
Convert the following binary values to hexadecimal
- 1011 1101
- 1010 0110
- 1111 1010 1100 1110
- 1011 1101 = BD
- 1010 0110 = A6
- 1111 1010 1100 1110 = FACE
Convert the hex value AB to Denary
171
Convert the denary value 166 to hexadecimal
A6
Convert the following denary values to hexadecimal
- 22
- 42
- 170
- 22 = 16
- 42 = 2A
- 170 = AA
Why do we use hexadecimal?
- Easier for programmers to read and understand
- Conversion to binary easier than denary to binary
- Takes up less space when displayed or printed
- Faster than binary for entering numbers
Where is Hexadecimal used?
- HTML colour codes e.g. red = #FF0000
- Display MAC (Media Access Control) addresses e.g. 01-23-45-67-89-AB-CD
- Display ASCII or Unicode values e.g. %41 = 65 = A
- Display error codes e.g. error #404 page not found
- Display memory dumps e.g. 5F 3A 09 F1
What is ASCII?
- American Standard Code for Information Interchange.
- It is a code for representing 128 English characters as numbers
- Each character is assigned a number from 0 to 127
How many bits does ASCII use?
7 bits
How many characters can be represented using ASCII?
- Uses 7 bits so …
- 000 0000 to 111 1111 = 0 to 127 = 128 unique characters (2^7)
How many bits does extended ASCII use?
8
How many characters can be represented using extended ASCII?
- 0000 0000 to 1111 1111 = 0 to 255 = 256 unique characters (2^8)
How many bits does Unicode use?
16
How many characters can be represented using Unicode?
- Uses 16 bits so … 65536 unique characters (2^16)
Describe the difference between ASCII and Unicode
- ASCII uses 7 (or 8 bits) and can represent 128 (or 256 characters)
- Unicode uses 16 bits and can represent 2^16 characters.
Describe one advantage of Unicode
Can represent a wider range of characters and therefore more languages than ASCII
Describe one disadvantage of Unicode
Each character uses more memory space than ASCII
Describe what is meant by a character set
- All the characters and symbols that can be represented by a computer system.
- Each character and symbol is assigned a unique value.
