The document discusses control units in basic computers. It describes hardwired control and microprogrammed control. Hardwired control generates signals using logic gates while microprogrammed control stores control information in a control memory. The control unit initiates sequential microoperations from the control memory. It consists of decoders, counters, and control logic. Arithmetic operations like addition, subtraction, multiplication and division are also summarized for different data types.

2. Control unit of Basic Computer
1.
2.
Hardwired Control : When the control signals are
generated by hardware using conventional logic design techniques like gates,flip-flop,
decoder and other digital circuit .
• it has the advantage that it can be optimized to produce a fast mode of operation
• Requires changes in the wiring among the various components
Micro programmed Control : In the micro programmed organization
the control information is stored in a control memory.
• The control memory is programmed to initiate the required sequence of micro
operations
• In the Micro programmed control any required changes or modifications be done
by updating the microprogram in control memory.

3. • Control Unit : Control unit in digital computer is to initiate
sequence of microoperations
• The control unit initiates a series of sequential steps of microoperation
during any given time certain microoperation are to be initiated ,while
other remain idle.
• It consists of two decoders ,a sequence counter, a number of control logic
gates.
• An introduction read from memory is placed in the instruction register(IR).
• The operation code in bits 12 through 14 are decoded with a 3 × 4
decoder .
• The eight output of the decoder are designated by the symbols D0
through D7.

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5. Microprogrammed control organization
A memory that is part of a control unit is called a control Memory.
A computer that uses a microprogrammed control unit usually has two
separate memories -
1.Main memory
2.Control memory.
Main memory
The main memory is available to the user for storing their programs. The
contents of main memory may change when the data are manipulated and
every time the program is changed. The user' program in main memory
consists of machine instructions and data.

6. Microprogrammed control organization
control memory holds a fixed microprogram that cannot be
altered by the occasional user. usually a ROM, which stores all control
information permanently
Microprogram Sequencer
A microprogram sequencer is the next address generator, as it determines the
address sequence that is read from control memory. The address of the next
microinstruction can be specified in several ways depending on the sequencer
inputs. The functions of a microprogram sequencer are incrementing the control
address register by one
Control data register (DR)
The control DR(data register) stores the present microinstruction while the next
address is computed and read from memory. The data register is also called a
pipeline register. It allows the execution of the microoperations specified by the
control word simultaneously with the generation of the next microinstruction

7. Microprogrammed control organization
Control Address Register holds the microinstruction read from memory. The
Microinstruction contains a control word that specifies one or more
microoperation for the data processor.
Instruction Format
Microinstruction format
The 20 bits of the microinstruction are divided into four functional parts.
The three fields F1, F2, and F3 specify microoperation for the computer.
CD: Condition for Branching
BR: Branch field
AD: Address field

13. Selection of Address for control Memory

18. Addition and Subtraction
We consider addition,subtraction,multiplication,and division
for the following types of data:
• Fixed-Point binary data in signed-magnitude
representation
• Fixed-Point binary data in signed-2’s compliment
representation
• Floating point binary data

19. Addition and Subtraction
A processor has an arithmetic processor(as a sub part of
it) that executes arithmetic operations. The data
type, assumed to reside in processor, registers during
the execution of an arithmetic instruction. Negative
numbers may be in a signed magnitude or signed
complement representation.
There are three ways of representing negative fixed point
- binary numbers
1.signed magnitude,
2. signed 1’s complement
2. Signed 2’s complement.
Most computers use the signed magnitude epresentation
for the mantissa

20. Addition and Subtraction With Signed-Magnitude Data
Addition and Subtraction With Signed-Magnitude Numbers

25. hardware implementation for signed magnitude
addition and subtraction
As and Bs is a sign flip-flop
Output carry is transferred to flip-flop E
AVF holdes the overflow bit

26. hardware implementation for signed magnitude
addition and subtraction
As and Bs is a sign flip-flop
Output carry is transferred to flip-flop E
AVF holdes the overflow bit

27. Flowchart for add and subtract operation

28. Addition and Subtraction With Signed-2’s Compliment
Data

29. Addition and Subtraction With Signed-2’s
Compliment Data
• The leftmost bit of a binary number represents the sign : 0 to
denote positive and 1 to denote negative.
• If the sign bit is 1, then we represent number in 2's
complement form.
• Thus + 33 is represented as 00100000 and -33 as
11011110. Note that 11011110 is the 2's complement of
00100000
• The addition of two numbers in signed 2's complement form
by adding the numbers with the sign bits treated the same
as the other bits of the number. We discard the carry of the
sign-bit position.
• The subtraction consists of first taking the 2's complement
of the subtrahend and then adding it to the minuend.

30. • We can detect an overflow by inspecting the last
two carries of the addition. When the two carries
are applied to an exclusive-OR gate, the verflow
is detected when the output of the gate is equal
to 1.

32. Multiplication Algorithm
Multiplication of two fixed-point binary numbers in signed magnitude representation

33. Hardware for Multiply operation

34. Multiplication Algorithm
• The multiplier is stored in the register
• and its sign in Qs.
• The sequence counter SC is initially set bits in
the multiplier. After forming each partial
product the counter is decremented. When
the content of the counter reaches zero, the
product is complete and we stop the process.

38. Booth multiplication algorithm
Booth algorithm needs examination of the multiplier bits and shifting of the
partial product. Prior to the shifting, the multiplicand added to the partial
product, subtracted from the partial product, or left unchanged by the
following rules:
1. The multiplicand is subtracted from the partial product when we get the first
least significant 1 in a string of 1' in the multiplier.
2. The multiplicand is added to the partial product when we get the first Q
(provided that there was a previous 1) in a string of 0' in the multiplier.
3. The partial product does not change when the multiplier bit is the same as
the previous multiplier bit.