cs240 Exam Final

cs240 Exam Final - Math Section Range = Base ^ N i.e. 16...

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Math Section Range = Base ^ N i.e. 16 bits (bits are base 2) has range of 2^16 = 64K 2^32 4G (billion) Binary Multiplication is shifting 110101 × 1001 110101 +110101000 Converting from Base to Decimal 13754 base8 to Decimal 8 4 × 1 + 8 3 × 3 + 8 2 × 7 + 8 1 × 5 + 8 0 (1) × 4 = 6124 Other Method Multiplying 1 ×8 = 8 + 3 = 11 11 ×8 = 88 + 7 = 95 95 × 8 = 760 + 5 = 765 765 × 8 = 6120 + 4 = 6124 Converting from Decimal to Base 6124 to Base5 Algorithmic Division 6124 / 5 = 1224 r 4 1224 / 5 = 244 r 4 244 / 5 = 48 r 4 48 / 5 = 9 r 3 9 / 5 = 1 r 4 1 / 5 = 0 r 1 =143444 Brute Force – divide by largest 5^n 6124 / 3125(or 5^5)= 1 2999 / 625(or 5^4) = 4 499 / 625(or 5^3) = 3 124 / 25(or 5^2) = 4 24 / 5( or 5^1) = 4 4 / 5^0 = 4 143444 base5 Related Bases Bases 2, 4, 8, 16… are related 0011 010 1 1101 1000 = 35D8 Hex, 32730 Octal, 113120 base4 Multiplication and Adding Hex (other bases’ principle is the same) F +F = 1E (15 + 15 = 30 – 16 (Next Place) = 14 (1E, 1(16) + 14)) F × F = E1 (15 × 15 =225 / 16 = 14 r1 remainder becomes 1s place, so E 1) Representing Numerical Data Binary Coded Decimal - BCD: represents each digit with 4 bits. i.e. 8 bit storage range would be 0 – 99, 99 =1001 1001, 50 =0101 0000, 8=0000 1000 Drawbacks are: - BCD has a range that is less than conventional binary representation -Calculations in BCD are more difficult for the computer thus slower Signed Integer Representation Changing the leftmost digit in Binary to a 0(+) or 1(-). This divides the bit range in half effectively, and creates the double zero problem. In addition, if the signs don’t agree, the result will be incorrect. i.e. 0…0100(4) + 1…0010(-2) = 1…0110 (-6) Overflow – when the result does not fit into the fixed # of bits for a result. If both inputs to an addition have the same sign and the output sign is different overflow has occurred. One’s Complement: Add two #s 01101010 = 106 +11111101 = -2 (+2 is 00000010, change 0’s to 1’s) 101100111 (carry over take the leftmost 1 and add it back) +1 01101000 = 104 Two’s Complement Positive # in One’s and Two’s complement are equal Negative # in two’s complement is found by writing the # in binary, inverting the digits and adding 1 i.e. Find -28 in Two’s 0001 1100 28 Binary +1 add 1 1110 0100 = -28 in Two’s Other complements – take each digit and subtract it from the # complement, i.e. 16s complement of 4C4D = F-2 F-C F-4 F-D or D3B2 Little Man Computer Take input IN 901 Print Output OU T 902 Store num to Address ST O 3xx Load num from Address LD A 5xx Add num in Address to accum AD D 1xx Sub num in Address from accum SU B 2xx Branch to address unconditionally BR 6xx Branch to address if accum value is 0 BR Z 7xx Branch if accum value is positive (0 is positive)
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This note was uploaded on 11/06/2011 for the course CS 240 taught by Professor Wong during the Fall '10 term at Bentley.

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cs240 Exam Final - Math Section Range = Base ^ N i.e. 16...

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