Question 2: [5 marks] a) [2] What is the greatest positive decimal integer value that could be stored in a 10-bit one's complement form? Give the actual number and explain briefly how you obtained it. b) [3] Determine the base b. You must demonstrate how you can get the value of b from basic principles (using algebra) rather than by trial and error. $(55)_b \times (61)_b = (2695)_b$
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The remaining 9 bits represent the magnitude. The largest positive number will have all 9 magnitude bits set to 1. This gives us $111111111_2$ for the magnitude. Converting this binary number to decimal: $1 \times 2^8 + 1 \times 2^7 + 1 \times 2^6 + 1 \times Show more…
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6. Convert the fixed-point binary number 1001.011 to decimal. A. 9.75 B. 9.062 C. 9.5 D. 9.375 E. 9.252 F. 9.0112 7. A k-bit number, when represented as a 2's complement quantity, represents values in the range A. -2^(k-1) to 2^(k-1)-1 B. -2^(k-1) to 2^k C. -(2^(k-1))-1 to 2^(k-1)-1 D. -(2^(k-1)) to 2^(k-1)-1 E. -2^k to 2^k F. -(2^(k-1))-1 to 2^(k-1)-1 G. -2^k to 2^(k-1)-1 H. -(2^(k-1))-1 to 2^(k-1) 8. Convert the 8-bit 2's complement binary number 11100010_2C to decimal. A. -226 B. -30 C. 30 D. 226 E. -29 F. 29 9. What is the 8-bit binary result from 2's complement addition below? 10110111 + 01101001 A. 0001 1110 B. 0010 0000 C. 0011 0000 D. 1101 1110 E. 1110 0000 F. 1110 0001
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