Question

Consider a hypothetical Control Unit which supports 8 k words. The Hardware contains 64 internal control signals, 16 bus control signals, 8 Flags and 8 branch conditions. What is the size of control word and control memory in: a) Horizontal Programming b) Vertical programming

Answer 1

Solution:

Given,

=>Number of control words memory = 8 K

=>Number of internal control signal = 64

=>Number of bus control signal = 16

=>Number of flags = 8

=>Number of branch conditions = 8

(a)

Explanation:

Horizontal programming:

Control word:

Branch condition

Internal control signal

Bus control signal

Flag

Memory

     3 bits                        64 bits                          16 bits              3 bits   13 bits

Calculaitng number of bits for branch condition:

=>Number of bits for branch condition = log₂(number of branch conditions)

=>Number of bits for branch condition = log₂(8)

=>Number of bits for branch condition = 3 bits

Calculating number of bits for internal control signal:

=>In horizontal programming 1 bit is required for each control signal.

=>Number of bits required for 64 internal control signal = 64 bits

Calculating number of bits for bus control signal:

=>In horizontal programming 1 bit is required for each control signal.

=>Number of bits required for 16 bus control signal = 16 bits

Calculating number of bits for flag:

=>Number of bits for flag = log₂(number of flags)

=>Number of bits for flag = log₂(8)

=>Number of bits for flag = 3 bits

Calculating number of bits for memory address:

=>Number of bits for memory address = log₂(size of memory)

=>Number of bits for memory address = log₂(8 K)

=>Number of bits for memory address = log₂(8*2^10)

=>Number of bits for memory address = 13 bits

Calculating size of control word:

=>Size of control word = 3 bits + 64 bits + 16 bits + 3 bits + 13 bits

=>Size of control word = 99 bits

Calculating size of control memory:

=>Size of control memory = (2^number of memory address bits)*size of control word

=>Size of control memory = 2^13*99 bits

(b)

Vertical programming:

Control word:

Branch condition

Internal control signal

Bus control signal

Flag

Memory

      3 bits                        6 bits                          4 bits              3 bits   13 bits

Calculaitng number of bits for branch condition:

=>Number of bits for branch condition = log₂(number of branch conditions)

=>Number of bits for branch condition = log₂(8)

=>Number of bits for branch condition = 3 bits

Calculating number of bits for internal control signal:

=>Number of bits required for 64 internal control signal = log₂(number of internal control signals)

=>Number of bits required for 64 internal control signal = log₂(64)

=>Number of bits required for 64 internal control signal = 6 bits

Calculating number of bits for bus control signal:

=>Number of bits required for 16 bus control signal = log₂(16)

=>Number of bits required for 16 bus control signal = 4 bits

Calculating number of bits for flag:

=>Number of bits for flag = log₂(number of flags)

=>Number of bits for flag = log₂(8)

=>Number of bits for flag = 3 bits

Calculating number of bits for memory address:

=>Number of bits for memory address = log₂(size of memory)

=>Number of bits for memory address = log₂(8 K)

=>Number of bits for memory address = log₂(8*2^10)

=>Number of bits for memory address = 13 bits

Calculating size of control word:

=>Size of control word = 3 bits + 6 bits + 4 bits + 3 bits + 13 bits

=>Size of control word = 29 bits

Calculating size of control memory:

=>Size of control memory = (2^number of memory address bits)*size of control word

=>Size of control memory = 2^13*29 bits

I have explained each and every part with the help of statements attached to it.