BINARY AND OTHER NUMBERING SYSTEMS Flashcards
WHAT ARE EVERYDAY NUMBERS IN?
BASE 10
HOW DO YOU COUNT UP TO THE NUMBER NINETY-NINE?
BY REPEATEDLY ADDING ONE TO THE UNITS COLUMN UNTIL NINE IS REACHED.
THEN BEGIN AT ZERO AGAIN
ADDING ONE TO THE TENS COLUMN
NUMBERING SYSTEMS
WHAT IS BINARYS BASE?
2
NUMBERING SYSTEMS
WHAT ARE BINARYS DIGITS?
0,1
NUMBERING SYSTEMS
WHAT IS OCTALS BASE?
8
NUMBERING SYSTEMS
WHAT ARE OCTALS DIGITS?
0,1,2,3,4,5,6,7
NUMBERING SYSTEMS
WHAT IS DECIMALS BASE?
10?
NUMBERING SYSTEMS
WHAT ARE DECIMALS DIGITS?
0,1,2,3,4,5,6,7,8,9
NUMBERING SYSTEMS
WHAT IS HEXADECIMALS BASE?
16
NUMBERING SYSTEMS
WHAT ARE HEXADECIMALS DIGITS?
0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
BINARY
WHAT IS BINARY?
A NUMBER SYSTEM THAT ONLY USES TWO DIGITS
1 AND 2
BINARY
WHAT IS BINARY BASED ON?
SWITCHES AND VALVES THAT HAVE TWO STATES
ON AND OFF
OPEN OR CLOSED
BINARY
HOW IS COMPUTER INFORMATION PROCESSED?
INFORMATION PROCESSED BY A COMPUTER IS IN THE FORM OF A SEQUENCE OF ONES AND ZEROS.
BINARY
WHAT MUST WE DO FOR INFORMATION THAT IS TO BE PROCESSED BY A COMPUTER?
CONVERT ALL DATA INTO BINARY
BINARY PLACE VALUES
2^7
128
BINARY PLACE VALUES
2^6
64
BINARY PLACE VALUES
2^5
32
BINARY PLACE VALUES
2^4
16
BINARY PLACE VALUES
2^3
8
BINARY PLACE VALUES
2^2
4
BINARY PLACE VALUES
2^1
2
BINARY PLACE VALUES
2^0
1
BINARY PLACE VALUES
2^-1
0.5
BINARY PLACE VALUES
2^-2
0.25
OCTAL
WHAT DOES BASE 8 MEAN?
THE SYSTEM ONLY USES 8 DIGITS FROM
0-7
OCTAL
WHAT IS IMPORTANT TO NOTE ABOUT THE PHYSICAL MEANING OF OCTAL NUMBERS?
THAT THE NUMBERS FROM 0-7 HAVE THE SAME PHYSICAL MEANING AS THAT OF DECIMAL NUMBERS
OCTAL
WHAT IS OCTAL USED BY?
OCTAL IS ANOTHER SYSTEM USED BY COMPUTERS WHEN THEY SENF INFORMATION.
OCTAL PLACE VALUES
8^7
2, 097, 152
OCTAL PLACE VALUES
8^6
262, 144
OCTAL PLACE VALUES
8^5
32, 768
OCTAL PLACE VALUES
8^4
4, 096
OCTAL PLACE VALUES
8^3
512
OCTAL PLACE VALUES
8^2
64
OCTAL PLACE VALUES
8^1
8
OCTAL PLACE VALUES
8^0
1
OCTAL
HOW TO WORK OUT AN OCTAL NUMBER
- 237₈
- 2 x 8 ² = 128 (TWO FROM THE HUNDREDS COLUMN, 8 FROM THE SUBSCRIPT AS ITS AN OCTAL NUMBER, TO THE POWER OF 2)
- 3 x 8 ¹ = 28 (THREE FROM THE TENS COLUMN, 8 FROM THE SUBSCRIPT AS ITS AN OCTAL NUMBER, TO THE POWER OF 1)
- 7 x 8⁰ = 7 (SEVEN FROM THE UNITS COLUMN, 8 FROM THE SUBSCRIPT AS ITS AN OCTAL NUMBER, TO THE POWER OF 0)
- 128 + 24 + 7 = 159₁₀ (SUBSCRIPT 10 AS IT IS NOW IN A BASE 10 DECIMAL
HEXADECIMAL
WHAT IS HEXADECIMAL?
HEXADECIMAL IS A BASE 16 NUMBERING SYSTEM.
HEXADECIMAL
WHAT IS THE HEXADECIMAL SYSTEM MADE UP OF?
- 16 DIGITS
- 0-9
- AND LETTERS
- A-F
HEXADECIMAL
WHY DOES THE HEXADECIMAL SYSTEM USE LETTERS?
- THE TEN DIGITS USED IN THE DECIMAL SYSTEM ARE NOT SUFFICIENT
- LETTERS ARE USED TO REPRESENT THE VALUES
- 10,11,12,13,14,15
WHAT DOES ₁₀ MEAN?
DECIMAL
WHAT DOES ₈ MEAN?
OCTAL
WHAT DOES ₁₆ MEAN?
HEXADECIMAL
WHAT DOES ₂ MEAN?
BINARY
WHAT ARE THE 4 NUMBERING SYSTEMS?
- BINARY
- OCTAL
- DECIMAL
- HEXADECIMAL
HEXADECIMAL PLACE VALUES
0
0
HEXADECIMAL PLACE VALUES
1
1
HEXADECIMAL PLACE VALUES
2
2
HEXADECIMAL PLACE VALUES
3
3
HEXADECIMAL PLACE VALUES
4
4
HEXADECIMAL PLACE VALUES
5
5
HEXADECIMAL PLACE VALUES
6
6
HEXADECIMAL PLACE VALUES
7
7
HEXADECIMAL PLACE VALUES
8
8
HEXADECIMAL PLACE VALUES
9
9
HEXADECIMAL PLACE VALUES
10
A
HEXADECIMAL PLACE VALUES
11
B
HEXADECIMAL PLACE VALUES
12
C
HEXADECIMAL PLACE VALUES
13
D
HEXADECIMAL PLACE VALUES
14
E
HEXADECIMAL PLACE VALUES
15
F
HEXADECIMAL
WHEN IS HEXADECIMAL NUMBERING SYSTEM USED?
BY PROGRAMMERS TO SIMPLIFY THE BINARY NUMBERING SYSTEM
HEXADECIMAL
HOW IS 16 EQUIVALENT TO 2⁴?
- 2√16=4
- 4 X 4 = 16
- THERE IS A LINEAR RELATIONSHIP BETWEEN 2 AND 16
HEXADECIMAL
WHAT IS THE RELATION BETWEEN HEXADECIMAL AND BINARY?
- EACH PLACE IN A HEXADECIMAL NUMBER REPRESENTS UP TO FOUR PLACES IN A BINARY NUMBER
- THE BINARY NUMBERS 0 - 1111 ARE REPRESENTED BY 0 TO F
HEXADECIMAL
WHAT PROGRAMMES ARE HEXADECIMAL USED IN?
- COLOUR REFERENCES
- ASSEMBLY LANGUAGE PROGRAMMES
- ERROR MESSAGES
HEXADECIMAL PLACE VALUES
16⁷
268, 435, 456
HEXADECIMAL PLACE VALUES
16⁶
16 777 216
HEXADECIMAL PLACE VALUES
16⁵
1 048 576
HEXADECIMAL PLACE VALUES
16⁴
65 536
HEXADECIMAL PLACE VALUES
16³
4096
HEXADECIMAL PLACE VALUES
16²
256
HEXADECIMAL PLACE VALUES
16¹
16
HEXADECIMAL PLACE VALUES
16⁰
1
HEXADECIMAL
HEXADECIMAL IS A PLACE VALUE SYSTEM; WHAT DOES THAT MEAN?
- EACH PLACE REPRESENTS A POWER OF 16
- THE PLACE REPRESENTS A POWER OF 10 IN THE DECIMAL SYSTEM