Question

homework # # FREE AS A "AA EVEVEJ -PA EEEEE Är 2 Abedre Autobate AaBbci ABCD ABCDE Due: In Class of Feb 19th, 20204 You must turn in a hardcopy of your work in class. Late homework and emailed homework will NOT be accepted. In all exercises, you need to SHOW ALL THE STEPS to obtain the results. Total 100 points 1. (10pts) Convert the following numbers from base 2 to base 10. a) 10110011 (base 2) b) 1101101 (base 2) 2. (10pts) Convert the following numbers from base 10 to base 2. a) 94 (base 10) - b) 134 (base 10) 3. (20pts) Arithmetic in binary. a) Perform the following binary addition. Show all the carries. 1110101001111 + 1110111111 b) Perform the following binary addition. Show all the carries. 1110110 1000011 + 11101 c) Perform the following binary multiplicatior. Show all the carries. 11011 * 101

Answer 1

1. a) (10110011)₂ = ( 1*2⁷ + 0*2⁶ + 1*2⁵ + 1*2⁴ + 0*2³ + 0*2² + 1*2¹ + 1*2⁰ ) = ( 128 + 0 + 32 + 16+ 2+ 1) = (179)₁₀

1. b) (1101101)₂ = ( 1 * 2⁶ + 1*2⁵ + 0*2⁴ + 1*2³ + 1*2² + 0*2¹ + 1*2⁰ ) = (64 + 32 + 0 + 8 + 4 + 1) = (109)₁₀

2. a)

(94)_{10 ==>} ( 94 % 2 ) = 0 ( 0 is Remainder for 92/2 )

(94 / 2) = 47 ==> ( 47 % 2 ) = 1

(47 / 2) = 23 ==> ( 23 % 2) = 1

(23 / 2) = 11 ==> ( 11 % 2) = 1

(11/ 2 ) = 5 ==> (5%2) = 1

(5/ 2 ) = 2 ==> (2 % 2 ) = 0

( 2/ 2) = 1 ( stop if x/2 is 0 or 1)

Writing the resultant remainders in buttom to up order : ( 1 0 1 1 1 1 0) ₂ .

2. b)

( 134 )₁₀ => (134 % 2) = 0

(134/ 2) = 67 ==> (67 % 2 ) = 1

(67 / 2 ) = 33 ==> ( 33 % 2) = 1

(33 / 2) = 16 ==> ( 16 % 2 ) = 0

(16/ 2) = 8 ==> ( 8 % 2) = 0

(8 / 2) = 4 ==> ( 4 % 2) = 0

( 4 / 2) = 2 ==> (2 % 2 ) = 0

( 2/ 2) = 1 ( stop if x/2 is 0 or 1)

Writing the resultant remainders in buttom to up order : ( 1 0 0 0 0 1 1 0) ₂ .

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