Lecture6

Lecture6 - Abhishek Bhattacharjee Topics: s Integer...

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Unformatted text preview: Abhishek Bhattacharjee Topics: s Integer Arithmetic 198:211 Computer Architecture Rutgers University Abhishek Bhattacharjee 2 Review Rutgers University 3 Abhishek Bhattacharjee Twos Complement 000 001 010 011 100 101 110 111 1 2 3-4-3-2-1 Ones complement plus one s Most significant bit still gives the sign s Trick: copy all 0 bits from LSB till first 1 bit. Copy 1 bit, then flip all remaining bits till MSB. Advantages: s Only 1 zero s Most convenient for arithmetic computations Used in almost all computers today Rutgers University Abhishek Bhattacharjee 4 IEEE floating point standard Most computers follow IEEE 754 standard Single precision (32 bits) Double precision (64 bits) Extended precision (80 bits) S Fraction Exponent Rutgers University Abhishek Bhattacharjee 5 Floating point in C 32 bits single precision (type float) s 1 bit for sign, 8 bits for exponent, 23 bits for mantissa c Sign bit: 1 = negative numbers, 0 = positive numbers c Exponent is power of 2 s Have 2 zeros s Range is approximately -10 38 to 10 38 64 bits double precision (type double) s 1 bit for sign, 11 bits for exponent, 52 bits for mantissa s Majority of new bits for mantissa b higher precision s Range is -10 308 to +10 308 Rutgers University Abhishek Bhattacharjee 6 Numerical Values Three different cases: s Normalized values c exponent field 0 and exponent field 2 k-1 (all 1s) c exponent = binary value Bias Bias = 2 k-1-1 (e.g., 127 for float) c mantissa = 1.(mantissa field) c Ex: (sign: 0, exp: 1, mantissa: 1) would give 0b1.1x2-126 s Denormalized values c exponent field = 0 c exponent = 1 Bias (e.g., -126 for float) c Mantissa = mantissa field (no leading 1) c Ex: (sign: 0, exp: 0, mantissa: 10) would give 0b10x2-126 s Special values: represent + , - , and NaN Rutgers University Abhishek Bhattacharjee 7 Decimal to IEEE Floating Point 5.625 In binary 101.101 b 1.01101 x 2 2 Exponent field has value 2...
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Lecture6 - Abhishek Bhattacharjee Topics: s Integer...

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