Lab 8 IEEE

1. Convert the number 7.231410 to IEEE 754 single precision format. a) The decimal to binary conversion Whole: 7 7/2 = 3R1 3/2 = 1R1 1/1 = 1R1 Whole in binary: 111 Fraction: 0.2314 0.2314*2 = 0.4628 0.4628*2 = 0.9256 0.9256*2 =1.8512 0.8512*2 =1.7024 0.7024*2 =1.4048 0.4048*2 =0.8096 0.8096*2 =1.6192 0.6192*2 =1.2384 0.2384*2 =0.4768 0.4768*2 =0.9536 0.9536*2 =1.9072 0.9072*2 =1.8144 0.8144*2 =1.6288 0.6288*2 =1.2576 0.2576*2 =0.5120 0.5120*2 =1.0240 0.0240*2 =0.0480 0.0480*2 =0.0960 0.0960*2 =0.1920 0.1920*2 =0.3840 0.3840*2 =0.7680 0.7680*2 =1.5360 0.5360*2 =1.0720 Fraction in binary: 00111011001111010000011 Answer:111.00111011001111010000011 2 b) How you normalized the number 1.1100111011001111010000011*2^2

0.9392*2 =1.8784 0.8784*2 =1.7568 0.7568*2 =1.5136 0.5136*2 =1.0272 0.0272*2 =0.0544 0.0544*2 =0.1088 0.1088*2 =0.2176 0.2176*2 =0.4352 Answer: 0.01010011000010111110000 2 b) How you normalized the number 1.010011000010111110000* 2 ^ -2 c) How you converted it to 8-bit excess-127 notation -2+127=125 01111101 d) How you converted the mantissa/significand to "hidden bit" format 010 1001 1000 0101 1111 0000 e) The sign bit 0 f) Result in binary (32-bits) 0011 1110 1010 1001 1000 0101 1111 0000 2 g) Result in Hexadecimal. 3 E A 9 8 5 F 0 16

3. Convert the number -3.2910 to IEEE 754 single precision format. a) The decimal to binary conversion Whole: 3 3/2 =1 R 1 1/2 =0 R 1 Whole Binary: 0011 Decimal: 2910 0. 2910*2 =0.5820 0.5820*2 =1.1640 0.1640*2 =0.3280 0.3280*2 =0.6560 0.6560*2 =1.3120 0.3120*2 =0.6240 0.6240*2 =1.2480 0.2480*2 =0.4960 0.4960*2 =0.9920 0.9920*2 =1.9840 0.9840*2 =1.9680 0.9680*2 =1.9360 0.9360*2 =1.8720 0.8720*2 =1.7440 0.7440*2 =1.4880 0.4880*2 =0.9760 0.9760*2 =1.9520 0.9520*2 =1.9040 0.9040*2 =1.8080 0.8080*2 =1.6160 0.6160*2 =1.2320 0.2320*2 =0.4640 0.4640*2 =0.9280 Decimal Binary: 01001010011111101111100 Answer: 11. 01001010011111101111100 2 b) How you normalized the number 1.101001010011111101111100 * 2 ^ 1

b) How you normalized the number 1.0101111001010 * 2 ^ 13 c) How you converted it to 8-bit excess-127 notation 13+127=140 =1000 1100 d) How you converted the mantissa/significand to "hidden bit" format 000 0000 0000 0000 0000 0000 e) The sign bit 1 f) Result in binary (32-bits) 1100 0110 0000 0000 0000 0000 0000 0000 g) Result in Hexadecimal. C 6 0 0 0 0 0 0 16 Time Spent : 2 hours 7min