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CSE 2353 Spring 2009

CSE 2353 Spring 2009. Number Systems. Number Systems. Normal everyday math is in base 10 (decimal numbers) Why? Computers function in base 2 (binary numbers) Why? When interpreting computer data, humans often use base 8 (octal) or base 16 (hexadecimal) Why?. Number Systems.

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CSE 2353 Spring 2009

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  1. CSE 2353 Spring 2009 Number Systems SMU - Dunham

  2. Number Systems • Normal everyday math is in base 10 (decimal numbers) • Why? • Computers function in base 2 (binary numbers) • Why? • When interpreting computer data, humans often use base 8 (octal) or base 16 (hexadecimal) • Why? SMU - Dunham

  3. Number Systems • Decimal numbers: 0,1,2,…,9 • Binary numbers: 0,1(Bit) SMU - Dunham

  4. Number Systems • Octal numbers: 0,1,…,7 Group binary by threes • Hexadecimal numbers: 0,1,2,…,9,A,B,C,D,E,F Group binary by fours SMU - Dunham

  5. In Class Exercises • Write the first 10 (in decimal) numbers in each number system. • Convert 110010 (binary) to decimal and octal and hexadecimal (Algorithm p 117). • Convert 3545 (decimal) to binary (Algorithm p116) and octal and hexadecimal • Convert 724 (octal) to binary and decimal and hexadecimal • Convert 5CE (hexadecimal) to binary and decimal and octal SMU - Dunham

  6. How is Data Represented? • What does 01010111 mean? • If an instruction, then the opcode indicates what it is • If not an instruction then must be interpreted differently: • Integer - Based on number system used by machine and instruction • Real - Based on how real numbers are stored for this machine and instruction • Character - Based on encoding scheme (ASCII, EBCDIC) SMU - Dunham

  7. Basic Integer Number Systems • Unsigned: 0 to • Sign Magnitude: to • High order bit indicates sign (0-positive; 1-negative) • Low order (n-1) bits indicates “number” • One’s Complement: • Positive same as sign magnitude • Negative number obtained by inverting all bits • Same range as sign magnitude SMU - Dunham

  8. Basic Integer Number Systems • Two’s Complement • Range: to • Positive same as sign magnitude • Leftmost bit is sign (0-positive, 1-negative) • Negative number: Invert bits and add 1 • 8088/8086 • Excess • Same range as two’s complement • Leftmost bit is sign (0-negative, 1-positive) SMU - Dunham

  9. Why Different Number Systems? • Range supported • Ease of operations • Number of zeros SMU - Dunham

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