Question No. 5: [5 Marks]
Convert the following by showing all the steps necessary
a) (1001111)2 = ( )10
b) (11000001)2 = ( )16
c) (E16)16 = ( )10
d) (56)10 = ( )16
e) (63)10 = ( )2
Rubrics (Scoring Guide)
- Steps = 80%
- Correct Answer = 20%
Answers
Answer:
hope it is helpful to you
Given : (1001111)2 = ( )10
(11000001)2 = ( )16
(E16)16 = ( )10
(56)10 = ( )16
(63)10 = ( )2
To Find : Fill in the Blanks
Solution:
(1001111)₂ = ( 79)₁₀
1 x 2⁶ + 0 x2⁵ + 0 x2⁴ + 1 x 2³ + 1 x 2² + 1 x 2¹ + 1 x 2⁰
= 64 + 0 + 0 + 8 + 4 + 2 + 1
= 79
(11000001)₂ = ( C1)₁₆
1 x2⁷ + 1 x 2⁶ + 0 x2⁵ + 0 x2⁴ + 0 x 2³ + 0 x 2² + 0 x 2¹ + 1 x 2⁰
= 128 + 64 + 0 + 0 + 0 + 0 + 0 + 1
= 193
Division by 16 Quotient Remainder Digit #
193/16 12 1 1
12/16 0 12 (C) 2
Hence ( C1)₁₆
(E16)₁₆ = ( 3606)₁₀ E is 14
14 x 16² + 1 x 16¹ + 6 x 16⁰
= 3584 + 16 + 6
= 3606
(56)₁₀ = (38 )₁₆
Division by 16 Quotient Remainder Digit #
56/16 3 8 1
3/16 0 3 2
Hence (38)₁₆
(63)₁₀ = (111111 )₂
Division by 2 Quotient Remainder Bit #
63/2 31 1 1
31/2 15 1 2
15/2 7 1 3
7/2 3 1 4
3/2 1 1 5
1/2 0 1 6
(111111 )₂
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