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HW3_solution - SOLUTION ECE 2504 Introduction to Computer...

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SOLUTION ECE 2504 Introduction to Computer Engineering, Fall 2009 Homework 3 Due date: 14 Sep 09, 11:55pm Show all work. 1. (5 pts) Convert (-275.53864) 10 to 32-bit floating point representation in standard IEEE format. Represent your answer in hex. 23 bit mantissa, 8 bit exponent 1 001 2 0 002 2 0 004 2 0 008 2 1 017 2 0 034 2 0 068 2 1 137 2 1 275 2 100010011 .53864 × 2 = 1. 07728 .07728 × 2 = 0. 15456 .15456 × 2 = 0. 30912 .30912 × 2 = 0. 61824 .61824 × 2 = 1. 23648 .23648 × 2 = 0. 47296 .47296 × 2 = 0. 94592 .94592 × 2 = 1. 89184 .89184 × 2 = 1. 78368 .78368 × 2 = 1. 56736 .56736 × 2 = 1. 13472 .13472 × 2 = 0. 26944 .26944 × 2 = 0. 53888 .53888 × 2 = 1. 07776 .07776 × 2 = 0. 15552 .15552 × 2 = 0. 31104 (0.100010011110010 …) 2 - 100010011.100010011110010 = - 1.00010011100010011110010 × 2 8 = (-1) 1 × 1.00010011100010011110010 × 2 8 S = 1 e = 8; E = 8 + 127 = 135 F = 00010011100010011110010 1 10000111 00010011100010011110010 1100 0011 1000 1001 1100 0100 1111 0010 C389C4F2H
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SOLUTION 2. (5 pts) Convert 42BBA400H, which is a 32-bit floating point number in IEEE 754 format, to decimal. 42BBA400H 0100 0010 1011 1011 1010 0100 0000 0000 0 10000101 01110111010010000000000 S = 0 E = 133; e = 133 – 127 = 6 F = 01110111010010000000000 (-1) 0 × 1.01110111010010000000000× 2 6 = + 1011101.11010010000000000 1×2 6 + 1×2 4 + 1×2 3 + 1×2 2 + 1×2 0 + 1×2 -1 + 1×2 -2 + 1×2 -4 + 1×2 -7 93.8203125 3. (4 pts) Represent the decimal number 5836 in BCD; excess-3 code; 2421 code; and in hex- coded binary. a. BCD: 0101 1000 0011 0110 b. XS-3: 1000 1011 0110 1001 c. 2421: 1011 1110 0011 1100 d. Binary: 1011011001100 Hex-coded binary: 16CC 1 0001 2 0 0002 2 1 0005 2 1 0011 2 0 0022 2 1 0045 2 1 0091 2 0 0182 2 0 0364 2 1 0729 2 1 1459 2 0 2918 2 0 5836 2
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