Question

You are given a decimal number to convert into binary. Press the buttons to

change their values so that the row represents the decimal number on the left.
When a 1 is used, we consider the value to be ON. When a 0 is used, we consider
the value to be OFF.

128
90
69
93
76
47
12
66
122
70
103

Answer 1

The binary representation of the given decimal numbers is:

1001000 quad 01011010 quad 01000101 quad 01011101 quad 01001100 quad 00101111 quad 00001100 quad 01000010 quad 01111010 quad 01000110 quad 01100111

Step-by-step explanation:

The binary conversion involves representing each decimal number in terms of powers of 2 determining the bits needed to sum up to the given decimal. Let's break down the conversion for the first number 128.

1.128 Decimal to Binary:

`\[ 128 = 2^7 \]`

Therefore the binary representation is 10000000 . The 1 is in the 128 place indicating it is ON while all other positions are OFF.

2.90 Decimal to Binary:

`\[ 90 = 2^6 + 2^4 + 2^3 + 2^1 \]`

So the binary representation is 01011010 The 1 bits are in positions 64 16 8 and 2 representing ON.

3. Repeat the process for the remaining numbers:

`\[ 69 = 2^6 + 2^3 + 2^2 + 2^0 \Rightarrow 01000101 \`]

`\[ 93 = 2^6 + 2^5 + 2^4 + 2^2 + 2^0 \Rightarrow 01011101 \]`

`\[ 76 = 2^6 + 2^4 + 2^2 \Rightarrow 01001100 \]`

`\[ 47 = 2^5 + 2^4 + 2^2 + 2^0 \Rightarrow 00101111 \]`

`\[ 12 = 2^3 + 2^2 \Rightarrow 00001100 \]`

`\[ 66 = 2^6 + 2^1 \Rightarrow 01000010 \]`

`\[ 122 = 2^6 + 2^5 + 2^4 + 2^3 + 2^1 \Rightarrow 01111010 \`

`\[ 70 = 2^6 + 2^4 + 2^2 + 2^1 \Rightarrow 01000110 \]`

`\[ 103 = 2^6 + 2^5 + 2^2 + 2^1 \Rightarrow 01100111 \]`

Combine these binary representations to obtain the final answer.

Answer 2

To convert the given decimal numbers into binary, here are their binary representations:

128: 10000000
90: 01011010
69: 01000101
93: 01011101
76: 01001100
47: 00101111
12: 00001100
66: 01000010
122: 01111010
70: 01000110
103: 01100111