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Octal and Hexadecimal, Number Systems, Digital Electronics 2014 Project Lead The Way Inc . What More Number Systems , Why do we need more number systems . Humans understand decimal, Check out my ten digits . Digital electronics computers understand binary. Since computers have 32 64 and even 128 bit busses displaying. numbers in binary is cumbersome , Data on a 32 bit data bus would look like the following . 0110 1001 0111 0001 0011 0100 1100 1010, Hexadecimal base 16 and octal base 8 number systems are.

used to represent binary data in a more compact form . This presentation will present an overview of the process for. converting numbers between the decimal number system and the. hexadecimal octal number systems 2, Converting To and From Decimal. 0123456789, Successive Weighted, Division Multiplication. Weighted Successive, Multiplication Division, Successive Weighted. Division Multiplication, Octal8 Hexadecimal16, 01234567 0123456789ABCDEF. Counting 2 8 10 16, Decimal Binary Octal Hexadecimal.

0 00000 0 0, 1 00001 1 1, 2 00010 2 2, 3 00011 3 3. 4 00100 4 4, 5 00101 5 5, 6 00110 6 6, 7 00111 7 7. 8 01000 10 8, 9 01001 11 9, 10 01010 12 A, 11 01011 13 B. 12 01100 14 C, 13 01101 15 D, 14 01110 16 E, 15 01111 17 F. 16 10000 20 10, 17 10001 21 11, 18 10010 22 12 4, 19 10011 23 13.

Review Decimal Binary, Base10 Successive, DECIMAL BINARY. a Divide the decimal number by 2 the remainder is the least significant bit. LSB of the binary number , b If the quotation is zero the conversion is complete Otherwise repeat step. a using the quotation as the decimal number The new remainder is the. next most significant bit MSB of the binary number . Base2 Weighted, Multiplication, BINARY DECIMAL, a Multiply each bit of the binary number by its corresponding bit weighting. factor i e Bit 0 20 1 Bit 1 21 2 Bit 2 22 4 etc . b Sum up all of the products in step a to get the decimal number . Conversion Process Decimal BaseN, Any base including Binary2 Octal8 Hexidecimal16 . Base10 Successive, DECIMAL ANY BASE, a Divide the decimal number by N the remainder is the least significant digit.

LSD of the ANY BASE Number , b If the quotient is zero the conversion is complete Otherwise repeat step. a using the quotient as the decimal number The new remainder is the. next most significant digit MSD of the ANY BASE number . BaseN Weighted, Multiplication, ANY BASE DECIMAL, a Multiply each bit of the ANY BASE number by its corresponding bit . weighting factor i e Bit 0 N0 Bit 1 N1 Bit 2 N2 etc . b Sum up all of the products in step a to get the decimal number . Decimal Octal Conversion, The Process Successive Division. Divide the decimal number by 8 the remainder is the least significant. digit LSD of the octal number , If the quotation is zero the conversion is complete Otherwise repeat. step a using the quotation as the decimal number The new. remainder is the next most significant digit MSD of the octal number . Convert the decimal number 9410 into its octal equivalent . 8 94 r 6 LSD, 1 9410 1368, 8 11 r 3, 8 1 r 1 MSD 7.

Example Decimal Octal, Convert the decimal number 18910 into its octal equivalent . Example Decimal Octal, Convert the decimal number 18910 into its octal equivalent . 8 189 r 5 LSD, 2 18910 2758, 8 23 r 7, 8 2 r 2 MSD. Octal Decimal Process, The Process Weighted Multiplication. Multiply each bit of the Octal Number by its corresponding bit . weighting factor i e Bit 0 80 1 Bit 1 81 8 Bit 2 82 64 . Sum up all of the products in step a to get the decimal number . Convert the octal number 1368 into its decimal equivalent . Bit Weighting 136 8 9410, 64 8 1 Factors, 64 24 6 9410.

Example Octal Dec, Convert the octal number 1348 into its decimal equivalent . Example Octal Decimal, Convert the octal number 1348 into its decimal equivalent . 1348 9210, 64 24 4 9210, Decimal Hexadecimal Conversion. The Process Successive Division, Divide the decimal number by 16 the remainder is the least. significant digit LSD of the hexadecimal number , If the quotation is zero the conversion is complete Otherwise.

repeat step a using the quotation as the decimal number The. new remainder is the next most significant digit MSD of the. hexadecimal number , Convert the decimal number 9410 into its hexadecimal equivalent . 16 94 r E LSD, 16 5 r 5 MSD 9410 5E16, Example Decimal Hex. Convert the decimal number 42910 into its hexadecimal equivalent . Example Decimal Hexadecimal, Convert the decimal number 42910 into its hexadecimal equivalent . 16 429 r D 13 LSD, 16 26 r A 10 42910 1AD16 1ADH, 16 1 r 1 MSD. Hexadecimal Decimal Process, The Process Weighted Multiplication.

Multiply each bit of the hexadecimal number by its. corresponding bit weighting factor i e Bit 0 160 1 Bit . 1 161 16 Bit 2 162 256 etc , Sum up all of the products in step a to get the decimal number . Convert the octal number 5E16 into its decimal equivalent . 161 160 5E 16 9410, Bit Weighting, 16 1 Factors, 80 14 9410. Example Hexadecimal Decimal, Convert the hexadecimal number B2EH into its decimal equivalent . Example Hexadecimal Decimal, Convert the hexadecimal number B2EH into its decimal equivalent . 162 161 160, B2EH 286210, 2816 32 14 286210, Example Hexadecimal Octal.

Convert the hexadecimal number 5AH into its octal equivalent . Example Hexadecimal Octal, Convert the hexadecimal number 5AH into its octal equivalent . First convert the hexadecimal number into its decimal equivalent . then convert the decimal number into its octal equivalent . 8 90 r 2 LSD, 8 11 r 3, 8 1 r 1 MSD, 80 10 9010, 5AH 1328 20. Example Octal Binary, Convert the octal number 1328 into its binary equivalent . Example Octal Binary, Convert the octal number 1328 into its binary equivalent . First convert the octal number into its decimal equivalent then. convert the decimal number into its binary equivalent . 2 90 r 0 LSD, 82 81 80 22, 2 45 r 1, 2 22 r 0 1328 10110102.

64 24 2 9010 5, 2 11 r 1, 2 5 r 1, 2 2 r 0, 2 1 r 1 MSD. Binary Octal Hex Shortcut, Because binary octal and hex number systems are all powers of two. which is the reason we use them there is a relationship that we can. exploit to make conversion easier , 1 0 1 1 0 1 0 2 132 8 5A H. To convert directly between binary and octal group the binary bits into. sets of 3 because 23 8 You may need to pad with leading zeros . 0 0 1 0 1 1 0 1 0 2 1 3 28, 1 3 2 001 011 010, To convert directly between binary and hexadecimal number systems . group the binary bits into sets of 4 because 24 16 You may need to. pad with leading zeros , 0 1 0 1 1 0 1 0 2 5 A 16, 5 A 0101 1 010 23.

Example Binary Octal Hex, Using the shortcut technique convert the hexadecimal number A616. into its binary and octal equivalent Use your calculator to check your. Example Binary Octal Hex, Using the shortcut technique convert the hexadecimal number A616. into its binary octal equivalent Use your calculator to check your. First convert the hexadecimal number into binary by expanding the. hexadecimal digits into binary groups of 4 , A616 101001102. Convert the binary number into octal by grouping the binary bits into. Hexadecimal (base 16) and octal (base 8) number systems are used to represent binary data in a more compact form. This presentation will present an overview of the process for converting numbers between the decimal number system and the hexadecimal & octal number systems.

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