2. Logic gates and binary numbers
Binary numbers (0 en 1)
Binary operators:
• AND: C = A • B
AND J C A B
• OR: C = A + B OR C A B
• NOT: A = -B NOT ÉL A B
Binary 170l n 1 23 1.22 0.2 1 20 13dec
Hexadecimal 123h 1 162 2.16 3.160 291sec
Conversions
bin
111 91
dec 17 2
hex B 2
To convert text into binary language, we use bytes. Characters like A-Z, a-z, 0-9 and
special characters must be encoded into specific binary chains. For this, we need to encode
about 100 symbols, which means we need at least 7 bits (2^7 = 128 ≥ 100). The standard
is to use 8 bits (= 1 byte).
• A byte is in fact one row of the RAM memory. A kilobyte is 1024 = 2^10 (≈ 10^3 ≈
1000) bytes
3. General structure of a computer
A computer consists of a Central Processing Unit (CPU), Memory Unit, and Input/Output (I/O)
devices.
The CPU interacts with memory unit. It consists of:
• Control Unit (CU): Manages machine cycle. Fetches next instruction from program counter
→ decodes information from instruction register
→ informs ALU to execute action
• Arithmetic/Logic unit (ALU): generates ‘new’ data
by doing calculations and computations. ALU is
comprised of logic gates (see Lecture 1)
• clock: Syncs busses
◦clock rate = machine cycles per second. A
higher clock rate means more instructions
per second → faster computer
, • registers: small memory unit (collection of flip-flops, usually 32-bit or 64-bit) within the
CPU for speed. Can serve a general or special purpose.
◦general: It holds data for ALU and stores its output (general purpose)
◦special: It holds instructions
‣ programm counter: adress to next instruction
‣ instruction register: current instruction to be executed
It is essentially a collection of transistors: electric semiconductors to amplify signals to
enable of disable.
In the RAM memory unit, logic gates are used in a transistor circuit (flip-flop) to store
information. It temporarily holds the data the processor just acted on or will act on soon.
Each row in memory is always 1 byte (= 8 bits). Also sequential instructions are stored here,
so that the CPU can immediately access them when the users opens a program. Each
memory cell has a value (8 bits) and an address. The more bits are in an adress, the
more rows of information can be stored: x bits means 2^x locations.
• For a 4GB RAM memory, you need an address of 32 bits: 4*2^30 = 2^2 * 2^30 = 2^32
• Long term holding of data is done in the storage (ROM). This belongs to the I/O unit.
It is not made of transistors, because it should hold data even when power is shut down
(non-volatile)
Input unit: to enter data into the computer (keyboard, mouse)
Output unit: to store information on a harddrive, or to show it on a monitor/screen
Data transfer goes through wires:
• data bus (information): bi-directional from and to CPU
• address bus (where should it go): memory address is put on address bus
• control bus (things that need to be processed to CPU): signals control transfer of data,
read/write request, complete transfer
Basic computer operations:
• receiving data/input
• storing data in memory
• performing mathematical and textual manipulations
• Comparing contents of two memory locations and choosing one (OR-logic)
• Repeating a group of operations (for- and while-loops)
• Executing information, processing data/output
