answer this and show answer step by step 1.7.1 Short Answer 1. In an 8-bit binar

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1.7.1 Short Answer 1. In an 8-bit binary number, which is the most significant bit (MSB)? 2. What is the decimal representation of each of the following unsigned binary integers? a. 00110101 b. 10010110 c. 11001100 3. What is the sum of each pair of binary integers? a. 10101111+ 11011011 c. 01110101 + 10101100 4. Calculate binary 00001101 minus 00000111. 5. How many bits are used by each of the following data types? a. word b. doubleword c. quadword d. double quadword unsigned decimal integers? a. 4095 b. 65534 c. 42319 7. What is the hexadecimal representation of each of the following binary numbers? a. 0011 0101 1101 1010 b. 1100 1110 1010 0011 8. What is the binary representation of the following hexadecimal numbers? a. 0126F9D4 b. 6ACDFA95 c. F69BDC2A

Explanation / Answer

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1. The rightmost digit is considered as the most significant bit as the change in this bit cause huge change in value of number. For example :

1010 = 10

0010 = 2 (changing msb, rightmost digit)

1011 = 11 ( changing lsb, leftmost digit)

2. 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. (20 = 1)

(a.) 00110101 = 0*27 + 0*26 + 1*25 + 1*24 + 0*23 + 1*22 + 0*21 + 1*20 = 32 + 16 + 4 + 1 = 53.

(b) 10010110 - 1*27 + 0*26 + 0*25 + 1*24 + 0*23 + 1*22 + 1*21 + 0*20 = 128 + 16 + 4 + 2 = 150.

(c) 11001100 - 1*27 + 1*26 + 0 + 0 + 1*23 + 1*22 + 0 + 0. = 204.

3. Rules for binary addition :

- 1 + 1 = 0 ( +1 carry)

- 1 + 0 = 1

- 0 + 0 = 0.

(a) 10101111

+ 11011011

-------------------------------------

110001010

(b) 10010111

+11111111

-----------------------------------

110010110

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