CST8110 Intro to Computing - Assignment #1Answer Key I

Always show the steps of your calculations for all conversions!

1. A x 0 = 00 A x 1 = 0A A x 2 = 14 A x 3 = 1E

A x 4 = 28 A x 5 = 32 A x 6 = 3C A x 7 = 46

A x 8 = 50 A x 9 = 5A A x A = 64 A x B = 6E

A x C = 78 A x D = 82 A x E = 8C A x F = 96

All digits and numbers above are Base 16.

2. 32,047(10) => 7 x 8**4 rem 3375

6 x 8**3 rem 303

4 x 8**2 rem 47

5 x 8**1 rem 7

7 x 8**0 rem 0 => 76457(8) octal

32,047(10) => 7 x 16**3 rem 3375

13 x 16**2 rem 47

2 x 16**1 rem 15

15 x 16**0 rem 0 => 7D2F(16) hexadecimal

32,047(10) => 7D2F(16) => 0111 1101 0010 1111(2) binary

3. Re-group the 16 binary bits by threes and by fours:

1 001 001 001 010 101(2) 1001 0010 0101 0101(2)

1 1 1 1 2 5(8) octal 9 2 5 5(16) hexadecimal

The number is negative, since the sign bit is set; but, that doesn’t affect conversions between bases 2, 8, and 16 where we simply group the bits differently. Only the conversion of a signed negative bit pattern to decimal needs the signed conversion method. We can convert the negative bit pattern to a negative decimal starting with any of binary, octal, or hexadecimal; let’s pick hexadecimal since it’s the shortest:

a) Invert the bits by subtracting 9255(16) from a 16-bit -1: (FFFF - 9255) => 6DAA(16)

b) Add 1 to complete the negation of the bit pattern: 6DAA + 1 = 6DAB(16)

c) Convert 6DAB(16) to decimal: B x 16**0 + A x 16**1 + D x 16**2 + 6 x 16**3 giving 28,075(10)

d) Changing the sign gives the correct negative decimal answer -28,075(10)