Section 2.3 General Positional Number System Conversions 27 Tabl 2-2 Conversion methods for common radices. Conversion Method Example Binary to Octal Substitution 101110110012=101110110012=2731g Hexadecimal Substitution 101110110012=101110110012=5D916 Decimal Summation 101110110012=1.1024+0.512+1.256+1.128+1.64 +0.32+1.16+1.8+0.4+0.2+1.1=149710 Octal to Binary Substitution 1234s =001 010 011 1002 Hexadecimal Substitution 1234s =001 010 011 1002=0010 1001 11002 =29C16 Decimal Summation 1234g=1.512+264+3.8+4.1=66810 Hexadecimal to Binary Substitution CODE16=1100 0000 1101 11102 Octal Substitution C0DE16=11000000110111102=11000000110111102=140336g Decimal Summation C0DE16=12.4096+0.256+13.16+14.1=4937410 Decimal to Binary Division 1082-54 remainder (LSB) +2-27 remainder( +2=13 remainder 1 +2=6 remainder 1 +2=3 remainder 0 +2=1 remainder 1 +2=0 remainder 1 (MSB) 10810=1101100: Octal Division 13 remainder 4 (least significant digit) +8=0 remainder I (most significant digit) 10810=154g Hexadecimal Division 1080+16=6 remainder 12 (least significant digit) +16=0 remainder 6 (most significant digit) 10810=6C16 Copyright1999 by John F.Wakerly Copying ProhibitedSection 2.3 General Positional Number System Conversions 27 DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY DO NOT COPY Copyright © 1999 by John F. Wakerly Copying Prohibited Table 2-2 Conversion methods for common radices. Conversion Method Example Binary to Octal Substitution 101110110012 = 10 111 011 0012 = 27318 Hexadecimal Substitution 101110110012 = 101 1101 10012 = 5D916 Decimal Summation 101110110012 = 1 ⋅ 1024 + 0 ⋅ 512 + 1 ⋅ 256 + 1 ⋅ 128 + 1 ⋅ 64 + 0 ⋅ 32 + 1 ⋅ 16 + 1 ⋅ 8 + 0 ⋅ 4 + 0 ⋅ 2 + 1 ⋅ 1 = 149710 Octal to Binary Substitution 12348 = 001 010 011 1002 Hexadecimal Substitution 12348 = 001 010 011 1002 = 0010 1001 11002 = 29C16 Decimal Summation 12348 = 1 ⋅ 512 + 2 ⋅ 64 + 3 ⋅ 8 + 4 ⋅ 1 = 66810 Hexadecimal to Binary Substitution C0DE16 = 1100 0000 1101 11102 Octal Substitution C0DE16 = 1100 0000 1101 11102 = 1 100 000 011 011 1102 = 1403368 Decimal Summation C0DE16 = 12 ⋅ 4096 + 0 ⋅ 256 + 13 ⋅ 16 + 14 ⋅ 1 = 4937410 Decimal to Binary Division 10810 ÷ 2 = 54 remainder 0 (LSB) ÷2 = 27 remainder 0 ÷2 = 13 remainder 1 ÷2 = 6 remainder 1 ÷2 = 3 remainder 0 ÷2 = 1 remainder 1 ÷2 = 0 remainder 1 (MSB) 10810 = 11011002 Octal Division 10810 ÷ 8 = 13 remainder 4 (least significant digit) ÷8 = 1 remainder 5 ÷8 = 0 remainder 1 (most significant digit) 10810 = 1548 Hexadecimal Division 10810 ÷ 16 = 6 remainder 12 (least significant digit) ÷16 = 0 remainder 6 (most significant digit) 10810 = 6C16