COMS 1004 homework 5

3) (6 points) Assume that the following 10-bit numbers represent signed integers using sign/magnitude notation. The sign is the leftmost bit and the remaining 9 bits represent the magnitude. What is the decimal value of each? ■ 0110011000 ■ 1000000001 ■ 1000000000 ● 0110011000 in decimal: The leftmost bit 0 is the sign bit -> positive integer The remaining 9 bits -> 110011000 0 ✕ 2 0 + 0 ✕ 2 1 + 0 ✕ 2 2 + 1 ✕ 2 3 + 1 ✕ 2 4 + 0 ✕ 2 5 + 0 ✕ 2 6 + 1 ✕ 2 7 + 1 ✕ 2 8 ¿ 0 + 0 + 0 + 8 + 16 + 0 + 0 + 128 + 256 ¿ 408 ● 1000000001 in decimal: The leftmost bit 1 is the sign bit -> negative integer The remaining 9 bits -> 000000001 1 ✕ 2 0 + 0 ✕ 2 1 + 0 ✕ 2 2 + 0 ✕ 2 3 + 0 ✕ 2 4 + 0 ✕ 2 5 + 0 ✕ 2 6 + 0 ✕ 2 7 + 0 ✕ 2 8 ¿ 1 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 /add the negative sign ¿ − 1 ● 1000000000 in decimal: The leftmost bit 1 is the sign bit -> negative integer The remaining 9 bits -> 000000000 0 ✕ 2 0 + 0 ✕ 2 1 + 0 ✕ 2 2 + 0 ✕ 2 3 + 0 ✕ 2 4 + 0 ✕ 2 5 + 0 ✕ 2 6 + 0 ✕ 2 7 + 0 ✕ 2 8 ¿ 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 /0 does not have a minus sign, but it’s included with the negative numbers in signed integer representation, so the decimal value is ¿ 0

7) (4 points) Using the ASCII table in the book (Appendix A), show the internal binary representation for the following character strings. ○ AbC ○ Joey ○ $23.00 ○ (a-b) Characte r string Each Character ASCII code Represented in binary AbC A, b, C 659867 010000010110001001000011 Joey J, o, e, y 74111101121 0100101001101111011001010111100 1 $23.00 $, 2, 3, ., 0, 0 365051464848 0010010000110010001100110010111 00011000000110000 (a-b) (, a, -, b, ) 4097459841 0010100001100001011011010010111 00110001000101001