ecse221_as1 - ECSE221Assignment#1 Question1 a i)15310=>N2...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
ECSE-221 Assignment #1 Question 1 a.) i.) 153 10  => N 2 Q 1  = 153/2 = 76 R = 1 Q 2  = 76/2 = 38 R = 0 Q 3  = 38/2 = 19 R = 0 Q 4  = 19/2 = 9 R = 1 Q = 9/2 = 4 R = 1 Q 6  = 4/2= 2 R = 0 Q 7  = 2/2= 1 R = 0 Q 8  = 1/2= 0 R = 1 Significant figures: d b  = d a  * (log a / log b) = 3 * (log 10 / log 2) = 9.97 ~ 10 Thus, 153 10  => 10011001 2 ii.) 153 10  => N 16 Using the binary form found above, separating into parts of 4: 10011001 => |1001|1001| - the binary parts correspond to 2 hex numbers (9 and 9) Significant figures: d b  = d a  * (log a / log b) = 3 * (log 10 / log 16) = 2.49 ~ 3 (2 is sufficient) Thus, 153 10  => 10011001 2  = 99 16 b.) i.) 100011101001 2   => N 16
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
As was done above, the binary is separated into groups of 4: 100011101001 2  => |1000|1110|1001| which corresponds to 3 hex numbers (8, 14 = E, 6) Significant figures: d b  = d a  * (log a / log b) = 12 * (log 2 / log 16) ~ 3  Thus, 100011101001 2  => 8E6 16 ii.) 100011101001 2  => N 10 Computing: 100011101001 2  = 1x2^0 + 1x2^3 + 1x2^5 + 1x2^6 + 1x2^7 + 1x2^11 = 2281 10 Significant figures: d b  = d a  * (log a / log b) = 12 * (log 2 / log 10) = 3.6 ~ 4  Thus, 100011101001 2  => 2281 10 iii.) 100011101001 2  => N 3 Using the decimal form found above,  Q 1  = 2281/3 = 760 R = 1 Q 2  = 760/3 = 253 R = 1 Q 3  = 253/3 = 84 R = 1 Q 4  = 84/3 = 28 R = 0 Q = 28/3 = 9 R = 1 Q 6  = 9/3= 3 R = 0 Q 7  = 3/3= 1 R = 0 Q 8  = 1/3= 0 R = 1
Background image of page 2
Significant figures: d b  = d a  * (log a / log b) = 12 * (log 2 / log 3) = 7.57 ~ 8 Thus, 100011101001 2  => 10010111 3 c.) i.) A42.159 16  => N 2 Translating into binary groups of 4: A = 1010, 4 = 0100, 2 = 0010, 1 = 0001, 5 = 0101, 9 = 1001 So, |1010|0100|0010|.|0001|0101|1001|  Significant figures: d b  = d a  * (log a / log b) = 6 * (log 16 / log 2) ~ 24 Thus, A42.159 16  => 101001000010.000101011001 2 ii.) A42.159 16  => N 10 Computing: A42.159 16  => 10x16^2 + 4x16^1 + 2x16^0 + 1x16^(-1) + 5x16^(-2) + 9x16^(-3) =  2626.08423. .. Significant figures: d b  = d a  * (log a / log b) = 6 * (log 16 / log 10) = 7.22 ~ 8 Thus, A42.159 16  => 2626.0842 10   iii.) A42.159 16  => N 5 Converting the found decimal form: Q 1  = 2626/5 = 525 R = 1 Q 2  = 525/5 = 105 R = 0 Q 3  = 105/5 = 21 R = 0
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Q 4  = 21/5 = 4 R = 1 Q = 4/5 = 0 R = 4 Hence, A42 16  = 2626 10  = 41001 5 . Converting the fractional part 0.159 16  =   0.0842 10 : Significant figures: d b  = d a  * (log a / log b) = 6 * (log 16 / log 5) = 10.3 ~ 11 0.0842 = 0.0842 x (5/5) = 0.421x5^(-1)x(5/5) = 2.105x5^(-2) = 
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 12

ecse221_as1 - ECSE221Assignment#1 Question1 a i)15310=>N2...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online