Robotics Reference
In-Depth Information
Figure 7.
The Z1 computer in the apartment of Konrad Zuse's parents in 1936 (Courtesy
of Horst Zuse)
puter in the world based on
floating-point
binary numbers.
15
The Z3
was destroyed in a World War II bombing raid but a replica is on show
in the Deutsches Museum in Munich.
Around 1942 Zuse decided to build an even more powerful com-
puter designated the Z4. Based on his experiences with the Z1, Z2 and
Z3 machines, Zuse decided that the Z4 needed much more memory
than he had previously employed. He concluded that constructing the
memory from metal sheets was far less expensive than building a mem-
ory using relays and it was already clear to him that a memory of 1,024
words,
16
each of 32-bits, would, if it consisted of relays, be much too
big—he would need more than 32,000 relays (1,024
×
32). But Zuse's
mechanical memory system, which he had patented in 1936, worked
very reliably, and for 1,024 words the system did not need more than
35 cubic feet of space. Zuse also estimated the costs of one 32-bit word
of his mechanical memory as being only five Reichmarks, approximately
$2.50 in 1942.
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A floating point binary number looks like this: 11
.
2
3
. The 11 before the decimal point
1011
×
2
0
). The 1011 after the decimal point is the
binary for 11/16
ths
(because it represents 1
/
2
+
0
/
4
+
1
/
8
+
1
/
16). It is called a floating point
number because the decimal point moves as the power of 2 increases or decreases (in this case it is
2
3
)—as this power increases the decimal point moves to the left, as this power decreases the decimal
point moves to the right.
16
The memory in a computer system is often provided in blocks that are measurable as a power
of 2. Hence 1,024 words (i.e., 2
10
) rather than (say) 1,000.
2
1
is the binary for 3 (because it represents 1
×
+
1
×
