228-1 Computer Architecture and Technology
TU856-1 and TU858-1
Computer Architecture and Technology
(Week 4) Tutorial 3
Questions and Answers ( 1 )
How can we consider the use of binary to represent all instructions and data on a computer system?
The two-state number system can be compared with ‘relay’ components and ‘switching’ – which makes up hardware architecture at its most fundamental levels.
Questions and Answers ( 2 )
A discursive investigation of Two’s Complement and how that works mathematically (as a method for subtraction and division).
Two’s Complement number conversion: 110
I.E. how do you find the decimal -1 in 8-bit binary?
0000 00012 (This is decimal 1 in 8-bit binary)
Flip 1s to 0s and 0s to 1s to get One’s Complement
1111 1110
Add a binary 1 to this to get Two’s Complement
1111 1111 (This can represent -12)
Two’s Complement again
Two’s Complement numbers can be used in calculations by the computer to have the effect of subtraction.
A few more examples on the right
Questions and Answers ( 3 )
What use has octal as a number base?
The use of three-place number systems.
Example
Older mainframe computers from 1950 and early 1960s used 12-bit, 24-bit or 36-bit words. Divisible by 3, so 3-bit octal labels fitted them for calculations.
Questions and Answers ( 4 )
What use has hexadecimal as a number base?
The use of four-place number systems.
Example
Computers from 1960s onward use 16-bit, 32-bit or 64-bit words. Divisible by 4, so 4-bit hexadecimal labels fit them for calculations.
Typical Exam (Sub) Question For This Content
Question
Give a brief description of binary, octal and hexadecimal number representations.
Sample solution
Binary
Computing machines operate on electrical current and so use two states. We view these states as the numbers 0 and 1.
This is the binary representation and is called ‘Base 2’.
Whether in decimal or binary, the position of numbers delineate their quantity.
Solution continued
Octal
Grouping binary digits, for example, 010010101110011 into threes looks like this:
9,58710 = |010|010|101|110|0112
The Octal notation for representing Binary numbers uses groups of three bits:
The symbols that are used to represent each group are the same as the integer value of each group. By using these Octal symbols (0 – 7), the number can be expressed in a more compact form:
9,58710 = (2|2|5|6|3) 8
Solution continued
Hexadecimal
Suppose that we group the example binary digits 010010101110011 into fours. Then this might be written:
9,58710 = |0010|0101|0111|00112
Now the groups of four can be given different symbols.
There are 16 different combinations of four binary digits.
The symbols chosen are the common numerals (0 – 9) and the remaining six possible four-bit combinations are represented by the letters, A, B, C, D, E and F.
(10 marks)
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