The hardware - The Computing Universe: A Journey through a Revolution - page 30

Fig. 2.12. Truth table for bit-wise
adder.

A B R C

A R

0 0 0 0

0 1 1 0

1 0 1 0 B C

1 1 0 1

Fig. 2.13. A half-adder made by combin-
ing four logic gates.

A
B

A R

R

HA

B C

C

Fig. 2.14. A full adder made by compos-
ing two half-adders with an OR gate.

C

HA

A

C
A
B

C

C

FA

R R

HA

B

C

universal building blocks. These objects can then be combined to build a bit-
wise half-adder, which can then be used to build a full bit-wise adder, which
then can be used to build whole-word adders and so on. The second principle
is that of “functional abstraction.” We have seen how the early computers used
electromagnetic relays to implement logic gates and logical operations ( B.2.5 ,
Fig. 2.15 ).
The slow relays were soon replaced by the faster but unreliable vacuum
tubes, which in turn gave way to transistors and now to integrated circuits in
silicon. The important point is that the logical design of an adder is indepen-
dent of its implementation. In his delightful topic The Pattern in the Stone , the
computer architect Danny Hillis shows how you can make mechanical imple-
mentations of logic gates ( Fig. 2.16 ).

Fig. 2.15. The first binary adder,
consisting of two battery cells, wires,
two telephone relays, two light bulbs,
pieces of wire, and a switch made from
a tobacco tin.

The memory hierarchy

In order to be able to do something useful, computers need a mechanism
for storing numbers. A useful memory not only needs to store results of inter-
mediate calculations on some sort of digital scratch pad, but also needs to be

B.2.5. George Stibitz (1904-95). As is often the case in science, some of Claude Shannon's ideas
about relay circuits had been discovered independently around the same time. George Stibitz, a
physicist at Bell Telephone Laboratories, was a member of a group of mathematicians whose job
was to design relay-switching equipment for telephone exchanges. Stibitz also saw “the similarity
between circuit paths through relays and the binary notation for numbers.” B2 Over one weekend
in 1937, Stibitz wired up some relays to give the binary digits for the sum of two one-digit binary
numbers. His output was two lightbulbs, which lit up according to the result of the binary addi-
tion. He then designed more complicated circuits that could subtract, multiply, and divide. With
a Bell Labs engineer named Samuel Williams, Stibitz went on to build a machine with about four
hundred relays that could handle arithmetic on complex numbers.