HW2_solution

# HW2_solution - SOLUTION ECE 2504 Introduction to Computer...

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SOLUTION ECE 2504 Introduction to Computer Engineering, Fall 2009 Homework 2 Due date: 7 Sep 09, 11:55pm Show all work. 1. (4 pts) Find the decimal equivalent of the following two’s complement numbers: 1011001; 10000011; 01010101; 111110001 a. The first bit of 1011001 is a 1. it is a negative number. 1011001 is the 2’s complement of 0100111 1011001 = - [0100111] - [1×2 5 + 0×2 4 + 0×2 3 + 1×2 2 + 1×2 1 + 1×2 0 ] 10 = - [32 + 0 + 0 + 4 + 2 + 1] 10 = (- 39) 10 b. 10000011 is the 2’s complement of 01111101 10000011 = - [01111101] - [1×2 6 + 1×2 5 + 1×2 4 + 1×2 3 + 1×2 2 + 0×2 1 + 1×2 0 ] 10 = - [64 + 32 + 16 + 8 + 4 + 0 + 1] 10 = (- 125) 10 c. 01010101 is a positive number 01010101 1×2 6 + 0×2 5 + 1×2 4 + 0×2 3 + 1×2 2 + 0×2 1 + 1×2 0 = 64 + 0 + 16 + 0 + 4 + 0 + 1 = 85 10 d. 111110001 is the 2’s complement of 000001111 111110001 = - [000001111] - [0×2 7 + 0×2 6 + 0×2 5 + 0×2 4 + 1×2 3 + 1×2 2 + 1×2 1 + 1×2 0 ] = - [0 + 0 + 0 + 0 + 8 + 4 + 2 + 1] = (- 15) 10 2. (6 pts) Perform the subtraction of the following unsigned decimal numbers by taking the 10’s complement of the subtrahend: 6340 – 1522; 1874 – 7290; 45 – 75. a.

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HW2_solution - SOLUTION ECE 2504 Introduction to Computer...

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