This homework consists of 4 questions. For those questions specified by numbers,

Question

This homework consists of 4 questions. For those questions specified by numbers, please find the corresponding problems from Section 1.4 in your textbook. You can finid similar questions and answers in Chegg solutions book called (Introduction to Digtal Design 3rd edition), it might be the same questions and it answers I need to get the solution for each in steps in steps and clear plaese

1. (0.8 points)

            (a) Convert the following binary integer to decimal: 10101110112

(b) Convert the following decimal integer to an 8-bit binary number (Hint: if the binary number you convert to is shorter than 8 bits, append 0s in front of the most significant bit to make it 8 bits): 12110

(c) Convert the following binary number to hexadecimal: 110110001012

(d) Convert the following hexadecimal number to decimal: 5D816

2. (0.4 points) Problems 5.c and 5.d.

3. (0.4 points) Write out how each of the following two numbers will be stored using BCD 8421 code: (a) 752, (b) 396.

4. (0.4 points) Problem 13.a.iv and 13.b.ii.

Explanation / Answer

If you have any problem with the answer just let me know in the comments and I'll try to solve it as soon as possible Also we are required to do only 4 parts of a question and will do other if have free time.

1.(a). To find decimal from binary we first write binary number than multiply them to their corresponding 2xwhich starts from right from 0 and incremented by by at each number.

Example, 1010 = 1*23+ 0*22+ 1*21+ 0*20 = 8 + 2 =10.

Now 10101110112 = 1*29 + 0*28 + 1*27 + 0*26 + 1*25 + 1*24 + 1*23 + 0*22 + 1*21 + 1*20 =512 + 128 + 32 + 16 + 8 + 1= 699.

(b) For converting to binary from decimal, we start by dividing the number by 2 and binary bit is zero if remainder is 0 and 1 if the remainder is 1.

12110 Remainder

121/2 1

60/2 0

30/2 0

15/2 1

7/2 1

3/2 1

1 now reading from bottom to upside.

Answer is 01111001

(c) For binary to haxadecimal we divide the binary number in pair of 4 bits and write their hex value.

110110001012 = 0110 1100 0101

0110 = 6

1100 = C

0101 = 5.

Therefore 110110001012 = 6C5.

(d) To convert hex to decimal and we first convert hex to binary and then binary to decimal.

5D816 = 010111011000 = 1496.

Steps :

5D816, we start by separating each digit and writing its binary equivalent.

5 = 0101

D = 1101 (D = 13th element in hex = 1101, 13 in Binary = 1101)

8 = 1000

So we have 5D8 = 010111011000 (binary)

Now we have to convert binary to decimal, starting from rightmost digit and multiplying it with 20 and the incrementing power at each digit as we move to left side.

= 0*211 + 1*210 + 0*29+ 1*28 + 1*27 + 1*26 + 0*25 + 1*24 + 1*23+ 0*22 + 0*21 + 0*20

= 1024 + 256 + 128 + 64 + 16 + 8= 1496.

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