DUE DATE: / Mon SEPT 22 2008 (At Beginning of Class)

Computer Architecture

Exercise #8

(Fri Sept 19 2008)

Points: 24

Name: ______

Objective & Instructions
The objective of this exercise is to gain familiarity with number representations and conversions. Answer all questions appropriately. If you are not sure about the answer you may discuss it with your neighbor or your instructor. Note that in all of the following problems the intermediate steps are worth 3 points while the final answer is worth 1 point. Good Luck!
  1. Convert 3610 to octal

Conversion is performed via successive divisions by 8 and writing the remainders in a bottom up fashion as shown below:

8 / 36
4 / 4

3610 = 448.

  1. Convert 1108 to decimal.

The conversion is performed by multiplying each digit (from right to left) with increasing powers of 8 and adding them together.

1108 = (1*82) + (1*81) + (0*80)

= (1*64) + (1*8) + (0*1)

= 64 + 8 + 0

= 7210

  1. Convert 10F16 to decimal.

The conversion is performed by multiplying each digit (rewriting hexadecimal digits to decimal values) from right to left with increasing powers of 16 and adding them together.

10F16 = (1*162) + (0*161) + (15*160) [Note F16 = 1510]

= (1*256) + (0*16) + (15*1)

= 256 + 0 + 1

= 25710

  1. Convert ABC16 to binary

The conversion is performed by writing 4-bit binary representation for each hexadecimal digit as shown below. The decimal values corresponding to each hexadecimal digit is shown to aid understanding (you need not include decimal values when you do the conversions).

Hex / A16 / B16 / C16
Decimal / 1010 / 1110 / 1210
Binary / 10102 / 10112 / 11002

ABC16 = 1010101111002

  1. Convert ABC16 to binary

This conversion is performed by grouping 4-bits at a time from right to left and writing the hexadecimal digit for each group of 4-bits.

Binary / 1102 / 10012 / 01012 / 00112
Hex / 616 / 916 / 516 / 316

1101001010100112 = 695316

  1. Convert 100111112 to Hex

This conversion is performed by grouping 4-bits at a time from right to left and writing the hexadecimal digit for each group of 4-bits.

Binary / 10012 / 11112
Decimal / 910 / 1510
Hex / 916 / F16

100111112=9F16

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