tutLN2soln

# tutLN2soln - FIT1001 Data Representation Solutions to...

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Unformatted text preview: FIT1001 Data Representation Solutions to FIT1001 Tutorials for LN2 Data Representation Data Representation – Integers (* Important to complete) Exercise 1 Convert the following fractions to binary: (a) 237.25 SOLUTION: • Integer part as usual 11101101 • Fraction: . 25 × 2 = 0 . 5 ⇒ remove the 0 . 5 × 2 = 1 . ⇒ remove the 1 . 01 result = 11101101.01 (b) 32.32 SOLUTION: • Integer part as usual 100000 • Fraction: . 32 × 2 = 0 . 64 ⇒ remove the 0 . 64 × 2 = 1 . 28 ⇒ remove the 1 . 28 × 2 = 0 . 56 ⇒ remove the 0 . 56 × 2 = 1 . 12 ⇒ remove the 1 . 12 × 2 = 0 . 24 ⇒ remove the 0 . 24 × 2 = 0 . 48 ⇒ remove the 0 . 48 × 2 = 0 . 96 ⇒ remove the 0 . 96 × 2 = 1 . 92 ⇒ remove the 1 . 92 × 2 = 1 . 84 ⇒ remove the 1 . . . . 010100011 . . . result = 100000.010100011 1 * Exercise 2 Represent the number- 92 in (a) 8-bit signed magnitude SOLUTION: Just convert +92 to binary (getting 01011100) and put sign bit 1 out the front to get- 92 (11011100). Here we don’t need to pad with leading 0s, but remind the students of need to do that in order to get required number of bits. (b) 8-bit 2’s complement SOLUTION: Again, start with +92 in 8 bits. (For +ve numbers, signed magnitude is same as 2’s complement. For NEGATIVE numbers, they are quite different.) Then negate, by complementing each bit then numerically adding 1. 10100011+1 = 10100100 (c) 8-bit excess-k SOLUTION: k = 2 7- 1 = 127- 92 + 127 = 35 00100011 * Exercise 3 Convert the following numbers from unsigned binary notation to decimal notation, and from 6-bit 2’s complement notation to decimal notation: SOLUTION: Unsigned binary (a) 110011 = 2 5 + 2 4 + 2 1 + 2 = 32 + 16 + 2 + 1 = 51 (b) 001101 = 2 3 + 2 2 + 2 = 8 + 4 + 1 = 13 (c) 100100 = 2 5 + 2 2 = 32 + 4 = 36 Two’s complement (verify using different conversion methods) (a) 110011 =- 2 5 + 2 4 + 2 1 + 2 =- 32 + 16 + 2 + 1 =- 13 (b) 001101 = 13 as above (c) 100100 ⇒ invert + 1 = 011011 + 1 = 011100 =- (2 4 + 2 3 + 2 2 ) =- (16 + 8 + 4) =- 28 2 Exercise 4...
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tutLN2soln - FIT1001 Data Representation Solutions to...

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