Maths and the History of ICT

Charles Babbage

• 1791-1871• English• Mathematician

and Philosopher• Originated the

concept of a programmable computer

Computers

In Babbage’s day a ‘computer’ was a person who was good at arithmetic and was employed to work out the results of calculations.

There were many errors, so Babbage set out to build a machine that could do the calculations. It used the concept of ‘finite differences’ so avoided the need for multiplication and division.

Babbage’s Difference Engine

Part of Babbage’s Difference Engine

Babbage’s Difference Engine

A Difference Engine built from Babbage’s design.It weighs 13600 kg.

Babbage’s BrainBabbage died at the age of 79. His brain was cut in two. Half of it is preserved at the Hunterian Museum in the Royal College of Surgeons in London. The other half is on display in the Science Museum, London.

Ada Lovelace

• 1815-1852• English• Writer• Daughter of poet

Lord Byron• The first computer

programmer

Ada LovelaceAlthough she never saw Babbage’s Difference Engine completed, she wrote the first computer program for it for finding Bernoulli Numbers.

In 1980 a computer language used by the US Department of Defence was named after her: ‘Ada’.

March 24 is commemorated by some as Ada Lovelace Day. This is a day to celebrate the achievements of woman in technology and science.

George Boole

• 1815-1864• English• Contributed to:– Logic– Maths philosophy

• Married daughter of George Everest

• Developed Boolean Logic

Boolean LogicThis is a special algebra which uses the values 1 and 0 only. These values 1 and 0 are sometimes called ‘true’ and ‘false’.

There are a number of operations, the primary ones are:and &or ||not ¬xor (called exclusive-or)⊕

This logic is at the heart of your computer and helps it make decisions and do arithmetic.

Boolean LogicThe operations can be shown in ‘truth tables’. This is the truth table for the operation and:

p q p & qTrue True TrueTrue False FalseFalse True FalseFalse False False

The result is True when both p and q are True.If 1s and 0s are used it is the same as multiplication

Boolean LogicThis is the truth table for the operation or:

p q p || qTrue True TrueTrue False TrueFalse True TrueFalse False False

The result is True when either p or q are True.

Boolean LogicThis is the truth table for the operation not:

p ¬pTrue FalseFalse True

The result is the opposite of p.

Boolean LogicThis is the truth table for the operation xor:

p q p ⊕ qTrue True FalseTrue False TrueFalse True TrueFalse False False

The result is True when either p or q are True but not when they are both True.

Boolean LogicSome combinations of operations can be show to be equivalent to other combinations.

p q ¬(p & q) ¬p || ¬qTrue True False FalseTrue False True TrueFalse True True TrueFalse False True True

This combination is called NAND (i.e. not and)

Alan Turing

• 1912-1954• English• Contributed to:

– Logic– Cryptanalysis– Computing

• Broke war codes created by the German ‘Enigma’ machine

• Significant in creation of the modern computer

Bombe