The ENGLISH ELECTRIC Co. Ltd.

NELSON RESEARCH LABORATORIES Technical Memorandum: NS u 242 STAFFORD Date: 9/9/57 MATHEMATICS DEPARTMENT Tel. Stafford 700Notes 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 addition not a multiplication)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 Therefore, answer = 123456789 (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