Assignment #1– Digital Logic Q1[Systems]> Please give an example for a sequential system from your daily life. Provide an I/O (input/output) description for your system and explain why your system is sequential. Q2[Base conversion]> Please answer the following questions by also showing the intermediate steps of your work: (1011001110010011)2 = ( ? )8 = ( ? )16 001 011 001 110 010 011 = (131623)8 1011 0011 1001 0011 = (B393)16 (734012)8 = ( ? )16 (734012)8 = (111011100000001010)2 (0011 1011 1000 0000 1010)2 = (3B80A)16 (54??53?)8 = (??6D?E)16 //Here, every ‘?’ corresponds to a digit (54??53?)8 = 101100??????101011??? (??6D?E)16 = ????????01101101????1110 0001 0110 0110 1101 0101 1110 = (166D5E)16 101 100 110 110 101 011 110 = (5466536)8 Q3[Two’s complement]> Please answer the following questions by also showing the intermediate steps of your work. Every ‘?’ represents a bit. From the third bullet onwards, the number on the left hand side of the equation is decimal: To two’s complement a number invert all the bits and then add 1 to the result → most significant bit 1 = negative number What is the range (smallest and largest decimal numbers) with 10-bit representation? o Signed = -512 to 512 o Unsigned = 0 to 1023 (210 - 1) ?01?001? is a positive binary number whose two’s complement is ?1?01110. What is the decimal equivalent of the first number? -23 = (??????)2 = (101001)2 -1*25 + 0*24 + 1*23 + 0*22 + 0*21 + 1*20 = -32+8+1 = -23 -23 = (????)3 = (1011)3 -1*33 + 0*32 + 1*31 + 1*30 = - 27 + 3 + 1 -127 = (????????)2 = (10000001)2 -1*27 + 0*26 + 0*25 + 0*24 + 0*23 + 0*22 + 0*21 + 1*20 = - 128 + 1 -127 = (?????????)2 = (110000001)2 -1*28 + 1*27 + 0*26 + 0*25 + 0*24 + 0*23 + 0*22 + 0*21 + 1*20 = - 256 + 128 + 1 -1 = (?????)2 = (11111)2 -1 = (??????????????????????????????????????????????????????)2 = (all 1)2 Q4[Binary arithmetic]> Please perform the following operation by showing the intermediate steps of your work; you need to show information regarding carry/borrow bits, and with BCD numbers, the intermediate binary representations and conditions being checked to produce carry/borrow: (10110111)2 + (11001011)2 = ( ? )2 1 1 + 1 1 1 1 0 1 0 1 1 0 0 //unsigned numbers 1 1 0 0 1 0 1 0 1 1 0 0 (00110111)2 - (10110000)2 = ( ? )2 1 1 1 1 1 1 0 //unsigned numbers 1 0 0 1 1 0 1 0 (00110111)2 + (11001011)2 = ( ? )2 1 0 + 1 1 0 1 1 0 0 (10110000)2 - (01110111)2 = ( ? )2 1 2 2 1 0 1 1 + 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 2 0 1 1 //signed numbers 1 1 0 0 1 0 1 0 1 1 0 0 1 1 1 1 1 1 0 //signed numbers 1 1 1 1 0 1 0 0 1 1 1 1 + 1 0 1 0 1 0 0 0 0 1 0 0 + 0 1 1 0 1 1 1 0 1 1 1 0 1 0 0 0 0 0 0 0 1 1 1 Overflow (1101)2 x (0101)2 = ( ? )2 (4624)BCD + (9318)BCD = ( 13942 )BCD 0 + 1 1 + 0 1 0 1 0 1 1 0 0 0 0 1 1 //unsigned numbers 0 1 1 0 1 1 0 1 1 0 + 0 0 1 1 1 0 0 1 1 0 0 + 0 0 0 1 1 1 0 0 1 0 1 0 0 + 1 1 + 0 0 1 0 1 1 0 0 0 0 1 1 0 0 0 0 0 1 3 9 4 2 BCD addition → subtracting 10 is same as adding 6 modulo 16 → carry gives us the 2nd digit of the addition (9318)BCD - (4624)BCD = ( ? )BCD 9’s complement of subtrahend: 9999 – 4624 = 5375 1 9 3 1 8 + 5 3 7 5 1 4 6 9 3 + 1 4 6 9 4