2.10 Convert the decimal number-35 to an 8-bit two\'s complement binary number 2

Question

2.10 Convert the decimal number-35 to an 8-bit two's complement binary number 2.11 Convert the decimal number -32 to an 8-bit two's complement binary number. 2.12 Assuming the use of the two's complement number system find the equivalent decimal values for the following 8-bit binary numbers: (a) 10000001 (c) 01010000 (d) 11100000 (e) 10000011 2.13 Convert the base 8 number 204 to decimal 2.14 Convert the base 7 number 204 to decimal 2.15 Convert the base 6 number 204 to decimal 2.16 Convert the base 5 number 204 to decimal 2.17 Convert the base 10 number 81 to a base 9 number.

Explanation / Answer

2.10)

First convert the decimal number to binary number by dividing by 2 with remainder

35 /2 remainder 1

17 /2 remainder 1

08 /2 remainder 0

04 /2 remainder 0

02 /2 remainder 0

01 /2 remainder 1

i.e. 100011

now to make it 8 -bit prefix it with 0

00100011

Binary Equivalent of +35. A preceding 00 had to be added to make it an 8 bit number. We must now take the two's compliment of this number because the original number (- 35) was negative

For two's complement, invert the digits. 0 becomes 1, 1 becomes 0.
11011100
Then we add 1
11011101

2.11)

First convert the decimal number to binary number by dividing by 2 with remainder

32 /2 remainder 0

16 /2 remainder 0

08 /2 remainder 0

04 /2 remainder 0

02 /2 remainder 0

01 /2 remainder 1

i.e. 100000

now to make it 8 -bit prefix it with 0

00100000

Binary Equivalent of +35. A preceding 00 had to be added to make it an 8 bit number. We must now take the two's compliment of this number because the original number (- 35) was negative

For two's complement, invert the digits. 0 becomes 1, 1 becomes 0.
11011111
Then we add 1
11100000

2.13)

To convert the base 8, process the digit from left to right, keeping a total you initialize at zero. For each digit x, set the total to 8*total+x. After processing the last digit, the total will be the base ten value of the base 8 sequence.

204 - we have total=2 (initialized at 0) digits

2 * 82 + 0 * 81 + 4 * 80 = 128+0+4 = 132

2.14)

To convert the base 7, process the digit from left to right, keeping a total you initialize at zero. For each digit x, set the total to 7*total+x. After processing the last digit, the total will be the base ten value of the base 7 sequence.

204 - we have total=2 (initialized at 0) digits

2 * 72 + 0 * 71 + 4 * 70 = 98+0+4 = 102

2.15)

To convert the base 6, process the digit from left to right, keeping a total you initialize at zero. For each digit x, set the total to 6*total+x. After processing the last digit, the total will be the base ten value of the base 6 sequence.

204 - we have total=2 (initialized at 0) digits

2 * 62 + 0 * 61 + 4 * 60 = 72+0+4 = 76

2.16)

To convert the base 5, process the digit from left to right, keeping a total you initialize at zero. For each digit x, set the total to 5*total+x. After processing the last digit, the total will be the base ten value of the base 5 sequence.

204 - we have total=2 (initialized at 0) digits

2 * 52 + 0 * 51 + 4 * 50 = 50+0+4 = 54

2.17)

to convert the decimal number to base-9 number, we need to divide the decimal number by 9

81/9 => 9 remainder 0

09/9 => 1 remainder 0

so the base-9 number will be 100

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.