```	                 The ENGLISH ELECTRIC Co. Ltd.
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DEUCE CONTROL PANEL MANUAL
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NELSON RESEARCH LABORATORIES                     Technical Memorandum: NS u 242
STAFFORD                                                         Date: 9/9/57
MATHEMATICS DEPARTMENT
Tel. Stafford 700

Notes on Binary Decimal and Decimal Binary Conversion
(using Brunsviga)

Report by: C. Robinson.

1.   SUMMARY.

This report gives instructions for decimal to binary and binary to decimal
conversions, using a hand operated Brunsviga calculating machine.

2.   DECIMAL-BINARY.

(a) Decimal Integers.
Place integer at extreme right hand side of register. Multiply by 0.03125.
If last five figures of product are less than 0.75 divide the first two of these
figures by three and record (without round off).  If the last five figures are
greater than or equal to 0.75 divide first two of these figures by 3, subtract
1 and record.  Now transfer, losing last five figures.  Multiply again by
0.03125 and carry on.  When integral portion of number in accumulator is less
than 32, record and stop.

Example.   123456789

123456789 x 0.03125 = 3858024.65625    Record 21

3858024 x 0.03125 =  120563.25000    Record 8

120563 x 0.03125 =    3767.59375    Record 19

3707 x 0.03125 =     117.71875    Record 23

117 x 0.03125 =       3.65625    Record 21

Therefore 123456789 = 21, 8, 19, 23, 21, 3 (Chinese binary. Groups
of five binary digits.)

(b) Decimal Fractions.

Set number on extreme left hand side of register.  Multiply by 32 so that
when the result is transferred the integral portion of the answer is not
transferred.  Record the integral portion and carry on to the requisite number
of binary places.

Example.  Calculate Binary equivalent of 0.853012 to 25 b.p.

0.853012 x 32 = 27.296384    Record 27

0.296384 x 32 =  9.484288    Record 9

0.484288 x 32 = 15.497216    Record 15

0.497216 x 32 = 15.910912    Record 15

0.910912 x 32 = 29.149184    Record 29

Therefore    0.853023 = 29, 15, 15, 9, 27, 0    to 25 binary places.

3.   BINARY-DECIMAL.

(a) Binary integers.

Write down binary integer in usual form i.e. the decimal equivalent of each
group of five binary digits, most significant on the right. Take the most
significant group of five binary digits and multiply the decimal equivalent by
32, add the next significant group, transfer and multiply again by 32. Repeat
until least significant group has been added in (Note the last operation is an

Example.  Find decimal equivalent of the binary integer, 21, 8, 19, 23, 21, 3.

3 x 32 = 96           Add 21

117 x 32 = 3744         Add 23

3767 x 32 = 120544       Add 19

120563 x 32 = 3858016      Add 8

3858024 x 32 = 123456768    Add 21

(b) Binary Fractions.

Set least significant group on left hand side of register. Multiply by
0.03125. Transfer and add the next least significant group to the result as a
decimal integer.  Multiply by 0.03125 and continue.

Example.

Find decimal equivalent of the binary fraction 29, 15, 15, 9, 27.0.

29 x .03125 = 0.90625

15.90625 x .03125 = 0.4970703125

15.4970703125 x .03125 = 0.4842834472

.4842834472 x .03125 = 0.2963838577

27.2963838577 x .03125 = 0.8530119956 = 0.853012 rounded off.

Signed: C Robinson
MATHEMATICS DEPARTMENT
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