cst131 assignment 1-07

CST 131 Assignment 1

1. Write a 2-3 pages description on a figure that has greatly contributed to the computing field.

Please describe the person’s contribution in detail.

Answer :

Charles Babbage (1791-1871), a computer pioneer, designed the

first automatic computing engines and widely known as the Father

of Computers was born 26 December 1791 in London. He invented

computers but failed to build them. The father of Charles was a

rich man, so it was possible for Charles to receive instruction from

several elite schools and teachers during the course of his

elementary education. He was about eight when he had to move to a country school to recover

from a dangerous fever. Then, he joined King Edward VI Grammar School in Totnes, South

Devon, a thriving comprehensive school that's still operative today, but his fragile health status

forced him back to private teaching for a period. He finally joined a 30 student closed number

academy managed by Reverend Stephen Freeman. The academy had a big library, where

Babbage used to study mathematics by himself, and learned to love it. Babbage arrived at Trinity

College, Cambridge in October 1810. He had a big culture because he knew Lagrange, Leibniz,

Lacroix, Simpson and he was seriously disappointed about the math programs available at

Cambridge. So he with J.Herschel, G.Peacock, and other friends, decided to form the Analytical

Society.

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When, in 1812, Babbage transferred to Peterhouse, Cambridge where he was the best

mathematician; but he failed to graduate with honours. He received an honorary degree later,

without even being examinated, in 1814. Babbage sought a method by which mathematical

tables could be calculated mechanically, removing the high rate of human error. Three different

factors seem to have influenced him: a dislike of untidiness; his experience working on

logarithmic tables; and existing work on calculating machines carried out by Wilhelm Schickard,

Blaise Pascal, and Gottfried Leibniz. He first discussed the principles of a calculating engine in a

letter to Sir Humphry Davy in 1822.

Figure 1.1: Difference Engine

Babbage's machines were among the first mechanical computers, although they were not

actually completed, largely because of funding problems and personality issues. He directed the

building of some steam powered machines that achieved some success, suggesting that

calculations could be mechanized. Although Babbage's machines were mechanical and unwieldy,

their basic architecture was very similar to a modern computer. The data and program memory

were separated, operation was instruction based, the control unit could make conditional jumps

and the machine had a separate

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Figure 1.2 Analytical Engine

Design of computers

Babbage was inspired by Napier's logarithm tables and Napier's logs and bones. He

began to design a difference engine in 1821 which was a very large and complicated machine

intended for doing logarithmic calculations automatically. The device was based on the principle

that the difference between certain values of the expression at a certain stage becomes constant.

But it was difficult to make the machine parts accurate enough to prevent errors to occur, using

the technology available at that time. Encouraged by the work of difference engine, he began

design of another machine the analytical machine, which could carry out many different types of

calculations. Analytical engine used the concepts of Automatic Loom and Difference Engine.

The Analytical machine had five units- input, output, store, mill, and control. Store was

used for storing numbers and Mill was used to do the calculations by rotation of gears and

wheels. Control unit did the job of supervision of all other units. Working with him was a

mathematician Lady Ada Lovelace, who provided the input material in the form of programs.

Thus, Lady Ada Lovelace became known to the world as the first computer programmer. She

coded these programs on punch cards. Her contribution was so valuable that a language called

"Ada" was named after her.

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The two concepts implemented in this machine, which revolutionized the Computer era

in the following years are

1. The machine was able to compare quantities and then decide which of the sequences

to follow

2. The results of a calculation could alter the numbers and instructions already stored in

the machine.

Babbage devoted his last 37 years for the development of the analytical engine. His

machine was too ahead of the time of development. Lack of better technology leaded to

incomplete work of Babbage that time and he passed away in 1871 before he had completed his

work.

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2. Implement the following Boolean function with a multiplexer.

(a) F (A, B, C, D) = ∑ (0, 2, 5, 7, 11, 14)

Answer:

Step 1) A truth table is drawn for 8x1 multiplexer F (A, B, C, D) = ∑(0, 2, 5, 7, 11, 14)

A B C D F

0 0 0 0 1

0 0 0 1 0

0 0 1 0 1

0 0 1 1 0

0 1 0 0 0

0 1 0 1 1

0 1 1 0 0

0 1 1 1 1

1 0 0 0 0

1 0 0 1 0

1 0 1 0 0

1 0 1 1 1

1 1 0 0 0

1 1 0 1 0

1 1 1 0 1

1 1 1 1 0

Table 2.1 Truth table

5

7

1

3

5

C

AB

S0S1

S2

2

4

6

0D

0

8 X 1MUX


Step2) The inputs are determined as D',D',D,D,0,D,0,D based on the table below:

0 1 D

0 0 0

1 1 1

1 0 D'

Table 2.2

Step 3) The inputs are identified as D' = 0, 1, 7

D = 2, 3, 5

0 = 4, 6

Step 4) The diagram of the multiplexer implemented shown.

Figure 2.1 the diagram of the multiplexer implemented

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2. Implement the following Boolean function with a multiplexer.

(b) F (A, B, C, D) = П (3, 8, 12)

Answer:

Step 1) A truth table is drawn for 8x1 multiplexer

F (A, B, C, D) = П(3,8,12)=F (A,B,C,D)=(0,1,2,4,5,6,7,9,10,11,13,14,15)

A B C D F

0 0 0 0 1

0 0 0 1 1

0 0 1 0 1

0 0 1 1 0

0 1 0 0 1

0 1 0 1 1

0 1 1 0 1

0 1 1 1 1

1 0 0 0 0

1 0 0 1 1

1 0 1 0 1

1 0 1 1 1

1 1 0 0 0

1 1 0 1 1

1 1 1 0 1

1 1 1 1 1

Table 2.3 truth table

7

7

1

3

5

C

AB

S0S1

S2

2

4

6

01

D

8 X 1MUX


Step2) The inputs are determined as D',D',D,D,0,D,0,D based on the table below:

Table 2.4

Step 3) The inputs are identified as D = 4, 6

D'= 1

1 = 0, 2,3,57

Step 4) The diagram of the multiplexer implemented shown.

Figure 2.2 the diagram of the multiplexer implemented

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0 1 D

0 0 0

1 1 1

1 0 D'

Diff

Bout

Y

X


3. Design a half-subtractor circuit with inputs x and y and outputs Diff and Bout. The circuit

subtracts the bits x–y and places the difference in Diff and the borrow in Bout.

Figure 3.1: Half Subtractor.

Table 1: Truth Table

DIFFERENCE = XY + XY

BORROW = XY

The half subtractor is a combinational circuit. It is used to perform subtraction of

two bits. There are two input bits in the half subtractor (X and Y) and two output bits, a

difference DIFF = (X-Y) and a Borrow.

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X Y DIFF BORROW

0 0 0 0

1 0 1 0

0 1 1 1

1 1 0 0

cst131 assignment 1-07

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