Homework1 - ECE 3441 Homework#1 1 100 001 101 111 0102 4 1...

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ECE 3441 Homework #1 1. 100 001 101 111 . 010 2 1000 0110 1111 . 0100 2 4 1 5 7 . 2 8 8 6 F . 2 16 4*8 3 +1*8 2 +5*8+7+2/8= 2159.25 10 8*16 2 +6*16+15+4/16= 2159.25 10 2. 301 16 a 0 =13=D .12*16=1.92 a -1 =1 .92*16=14.72 a -2 =E 18 16 a 1 =2 .72*16=11.52 a -3 =B .52*16=8.32 a -4 =8 1 16 a 2 =1 .32*16=5.12 a -5 =5 .12*16=1.92 a -6 =1 (repeats) 301.12 10 =12D. 1EB85 16 1 2 D . 5 8 B E 1 16 0001 0010 1101 . 0101 1000 1011 1110 0001 2 3. 93 8 a 0 =5 .7*8=5.6 a -1 =5 .6*8=4.8 a -2 =4 11 8 a 1 =3 .8*8=6.4 a -3 =6 .4*8=3.2 a -4 =3 1 8 a 2 =1 .2*8=1.6 a -5 =1 .6*8=4.8 a -6 =4 (repeats) 93.70 10 =135.5 4631 8 1 3 5 . 5 1 3 6 4 8 001 011 101 . 101 001 011 110 100 2 4. 375.54 8 = 3*8 2 +7*8+5+5/8+4/64 = 253.6875 10 253 3 a 0 =1 .6875*3=2.0625 a -1 =2 .0625*3=.1875 a -2 =0 84 3 a 1 =0 .1875*3=.5625 a -3 =0 .5625*3=1.6875 a -4 =1 28 3 a 2 =1 .6875*3=2.0625 a -5 =2 (repeats) 9 3 a 3 =0 3 3 a 4 =0 375.54 8 =253.6875 10 = 100101. 2001 3 1 3 a 5 =1 5. To convert from base three to base nine, take groups of two base three digits and represent them as a single base nine digit. 01 21 02 21 . 20 21 10 3 1 7 2 7 . 6 7 3 9
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6. a) 12 10 = 001100 2 11 10 = 001011 2 110011 110100 +1 +1 110100 2 = -12 10 110101 2 = -11 10 110100 +110101 (1) 101001 -12 10 + (-11 10 ) = 101001 2 b) 10 10 = 001010 2 3 10 = 000011 2 110101 111100 +1 +1 110110 2 = -10 10 111101 2 = -3 10 110110 +111101 (1) 110011
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