<p> Exercises – Signed Binary Arithmetic – CSE 271 K. Dudeck</p><p>1. Determine the unsigned and signed decimal equivalent operations for the following binary operations. Also indicate if any of these equivalent operations generate an overflow condition.</p><p> a) 01101 b) 0110111 + 10010 + 0011100 ------</p><p> c) 10010 d) 11000001 - 11000 - 00110100 ------</p><p>2. Convert each of the following numbers into Signed 2’s Complement Binary Numbers. Use 8 bits for each conversion.</p><p> a) +10710 d) -1258</p><p> b) -6910 e) -112</p><p> c) –12510 f) +4C16</p><p>3. Suppose you have to write an assembly program that performs the following calculation:</p><p> y  x 2  30x 161</p><p>The input x is an UNSIGNED five-bit binary number.</p><p> a) What is the decimal range for input x?</p><p> b) What is the maximum positive value for y?</p><p> c) What is the maximum negative value for y?</p><p> d) How many bits will you need to allocate for the SIGNED result y?</p><p> e) Convert your decimal answers for parts b) and c) to SIGNED 2’s complement binary. Answers </p><p>(1) a) 111112 , 13 + 18 = 31 Unsigned 13 + -14 = -1 Signed</p><p> b) 10100112 , 55 + 28 = 83 Unsigned 55 + 28 = -45* Signed</p><p> c) 110102 , 18 – 24 = 26* Unsigned -14 – -8 = -6 Signed</p><p> d) 100011012 , 193 – 52 = 141 Unsigned -63 - +52 = -115 Signed (*-Overflow)</p><p>(2)</p><p> a) 01101011 b) 10111011 c) 10000011</p><p> d) 10101011 e) 11111101 f) 10110100</p><p>(3)</p><p> a) 0 31 b) 192 c) –64</p><p> d) 9 bits e) 192 = 011000000 , -64 = 111000000</p>