Question

Base Conversion
Learning binary and other numbering systems is an important skill for computer and software engineers. Write the following in decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16). Show your work by hand (don’t forget to scan your work and put it in your PDF). Scanners are available in certain labs on campus and the computer lab on the first floor of Parks Library. If you take a picture, be sure that it is easily readable. For clarification, you convert what is given into the three other versions.

Decimal
110
1010
4210
25510

Hexadecimal
F16
DF16
8116

Binary
100100112
1111112

Octal
228

Answer 1

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Answer 2

Let's convert the given numbers to their respective decimal (base 10), binary (base 2), octal (base 8), and hexadecimal (base 16) representations.

Decimal:

1. 110 (binary) = 1*(2^2) + 1*(2^1) + 0*(2^0) = 4 + 2 + 0 = 6

2. 1010 (binary) = 1*(2^3) + 0*(2^2) + 1*(2^1) + 0*(2^0) = 8 + 0 + 2 + 0 = 10

3. 42 (decimal) = 4*(10^1) + 2*(10^0) = 40 + 2 = 42

4. 255 (decimal) = 2*(10^2) + 5*(10^1) + 5*(10^0) = 200 + 50 + 5 = 255

Hexadecimal:

1. F (hexadecimal) = 15 (decimal)

2. DF (hexadecimal) = 13*(16^1) + 15*(16^0) = 208 + 15 = 223

3. 81 (hexadecimal) = 8*(16^1) + 1*(16^0) = 128 + 1 = 129

Binary:

1. 10010011 (binary) = 1*(2^7) + 0*(2^6) + 0*(2^5) + 1*(2^4) + 0*(2^3) + 0*(2^2) + 1*(2^1) + 1*(2^0) = 128 + 0 + 0 + 16 + 0 + 0 + 2 + 1 = 147

2. 11111 (binary) = 1*(2^4) + 1*(2^3) + 1*(2^2) + 1*(2^1) + 1*(2^0) = 16 + 8 + 4 + 2 + 1 = 31

Octal:

1. 228 (octal) = 2*(8^2) + 2*(8^1) + 8*(8^0) = 128 + 16 + 8 = 152

Please note that the work has been shown for each conversion.