# Binary & Hex Number Representations

# Video

# Key Takeways

**Base 2:**Binary numbers only consists of digits`0`

and`1`

.**Base 10:**Decimal numbers only consists of digits`0-9`

.**Base 16:**Hexadecimal (or Hex) numbers only consists of digits`0-9`

and`a-f`

.- Converting between Binary <–> Decimal
- Converting between Hex <–> Decimal
- Converting between Binary <–> Hex

# Video Addendum

and **true**

are actually equivalent to 1 and 0 respectively.**false**

# Assignment

- Fill out tables 0-3 below. Work out everything on paper (no calculators or computers allowed). If you feel shaky, Tables 4-6 provide supplemental practice.
- Fill out table 7.
- Write a function which returns the 3rd digit of the input. For example, an input of
`9872`

would return`9`

. An input of`1`

would return`0`

as`001`

is the same value as`1`

. Hint is below. - Write a function which takes in two inputs: A, B. (choose better names as you see fit). Return the B’th digit of A. For inputs:
`A=8972`

and`B=2`

, return`9`

as`9`

is the 2nd digit. The 0th digit is`2`

, 1st digit is`7`

and 3rd digit is`8`

. - Ask the user to input an
`unsigned int`

. Check if the user input a valid binary number. For example,`912`

is not a valid input as`9`

or`2`

are not binary digits. If its a valid binary, print out the decimal (not`float`

, but rather Base 10) value of the number they input. For example, input`1000`

would print out`8`

as Base 2`1000`

is Base 10`8`

.

## Hint #3

`399 / 100 == 3`

in C++ because remember `/`

only returns whole number part when working with the `int`

type.

## Hint #3

How can the `%`

operator help?

# Samples

## Table 0

Short hand | Decimal Value | Binary Value | Hex Value |
---|---|---|---|

2^{0} |
|||

2^{1} |
|||

2^{2} |
|||

2^{3} |
|||

2^{4} |
|||

2^{5} |
|||

2^{6} |
|||

2^{7} |
|||

2^{8} |
|||

2^{9} |
|||

2^{10} |

## Table 1

Decimal Value | Binary Value | Hex Value |
---|---|---|

432 | ||

773 | ||

650 | ||

819 | ||

878 | ||

824 | ||

408 | ||

772 | ||

650 | ||

533 | ||

345 | ||

232 | ||

34 | ||

401 | ||

230 | ||

620 | ||

145 | ||

404 | ||

790 | ||

861 | ||

238 | ||

946 | ||

558 | ||

168 | ||

264 | ||

260 | ||

497 | ||

489 | ||

132 | ||

120 |

## Table 2

Decimal Value | Binary Value | Hex Value |
---|---|---|

0b1010000110 | ||

0b101111000 | ||

0b1110111101 | ||

0b1001010000 | ||

0b1100010111 | ||

0b100101000 | ||

0b1000110011 | ||

0b1101101001 | ||

0b1000000100 | ||

0b1001100011 | ||

0b1000100111 | ||

0b10000100 | ||

0b1010010111 | ||

0b1101110101 | ||

0b1100101110 | ||

0b1010010100 | ||

0b1100010101 | ||

0b11100110 | ||

0b1011110101 | ||

0b110010010 | ||

0b101101111 | ||

0b1001011 | ||

0b1101101 | ||

0b1110001110 | ||

0b10010000 | ||

0b101110111 | ||

0b100001111 | ||

0b1101111100 | ||

0b1011100 | ||

0b11010000 |

## Table 3

Decimal Value | Binary Value | Hex Value |
---|---|---|

0x3E1 | ||

0xB6 | ||

0x44 | ||

0xAE | ||

0x64 | ||

0x2C | ||

0x1B0 | ||

0x157 | ||

0x1B1 | ||

0x297 | ||

0x1D8 | ||

0xBA | ||

0x23E | ||

0x1F0 | ||

0xA6 | ||

0xA1 | ||

0x34A | ||

0x2FE | ||

0x36A | ||

0x36E | ||

0x24E | ||

0xAA | ||

0x32B | ||

0x2E1 | ||

0x162 | ||

0x11 | ||

0x343 | ||

0x209 | ||

0x1EC | ||

0x138 |

## Table 4

Decimal Value | Binary Value | Hex Value |
---|---|---|

437 | ||

351 | ||

432 | ||

392 | ||

742 | ||

39 | ||

216 | ||

906 | ||

251 | ||

869 | ||

245 | ||

126 | ||

714 | ||

823 | ||

794 | ||

325 | ||

419 | ||

958 | ||

701 | ||

312 | ||

674 | ||

825 | ||

866 | ||

274 | ||

91 | ||

574 | ||

791 | ||

975 | ||

419 | ||

582 | ||

103 | ||

360 | ||

760 | ||

176 | ||

194 | ||

622 | ||

595 | ||

493 | ||

260 | ||

885 | ||

981 | ||

585 | ||

58 | ||

2 | ||

664 | ||

644 | ||

630 | ||

375 | ||

603 | ||

608 | ||

102 | ||

320 | ||

585 | ||

479 | ||

419 | ||

294 | ||

212 | ||

402 | ||

535 | ||

168 | ||

490 | ||

907 | ||

146 | ||

843 | ||

692 | ||

776 | ||

530 | ||

726 | ||

925 | ||

655 |

## Table 5

Decimal Value | Binary Value | Hex Value |
---|---|---|

0b1110101000 | ||

0b1011001110 | ||

0b1010000001 | ||

0b10110001 | ||

0b1101101000 | ||

0b1011100110 | ||

0b11001111 | ||

0b1111010111 | ||

0b1000101101 | ||

0b1101111101 | ||

0b1000100000 | ||

0b1101010101 | ||

0b1101000000 | ||

0b101010110 | ||

0b1111111 | ||

0b100011100 | ||

0b1101001111 | ||

0b110001011 | ||

0b1001011000 | ||

0b1010001000 | ||

0b101111010 | ||

0b1111001010 | ||

0b100011000 | ||

0b1100100111 | ||

0b1111011110 | ||

0b10100110 | ||

0b1101111111 | ||

0b1101000000 | ||

0b1010001011 | ||

0b111000100 | ||

0b1110111100 | ||

0b100000101 | ||

0b10000000 | ||

0b1110101100 | ||

0b1010111000 | ||

0b10001100 | ||

0b1101110111 | ||

0b1010110 | ||

0b101101 | ||

0b11100011 | ||

0b100110110 | ||

0b1101111100 | ||

0b1110010010 | ||

0b101101001 | ||

0b1011110000 | ||

0b101000001 | ||

0b1110111100 | ||

0b1110111010 | ||

0b100011001 | ||

0b100011001 | ||

0b1010010 | ||

0b1111010111 | ||

0b1000111 | ||

0b1110010101 | ||

0b11000011 | ||

0b1010001000 | ||

0b1111100001 | ||

0b110000110 | ||

0b1111 | ||

0b1001101 | ||

0b101111010 | ||

0b1001010000 | ||

0b110110010 | ||

0b1000000 | ||

0b1101101110 | ||

0b110100110 | ||

0b111110110 | ||

0b1101011001 | ||

0b10 | ||

0b101111101 |

## Table 6

Decimal Value | Binary Value | Hex Value |
---|---|---|

0x26A | ||

0x1D9 | ||

0xB1 | ||

0x128 | ||

0x355 | ||

0x373 | ||

0x2E3 | ||

0x65 | ||

0x3B | ||

0xFF | ||

0x18C | ||

0x1BC | ||

0x3C4 | ||

0x37E | ||

0x15B | ||

0x2F8 | ||

0xA4 | ||

0x92 | ||

0x27 | ||

0x309 | ||

0x3D7 | ||

0x259 | ||

0xCB | ||

0x118 | ||

0x3E2 | ||

0xF6 | ||

0x37C | ||

0x2F6 | ||

0x2B6 | ||

0x3DB | ||

0x140 | ||

0x2A1 | ||

0xB6 | ||

0x39A | ||

0x322 | ||

0x164 | ||

0x213 | ||

0x1E4 | ||

0x1B1 | ||

0x374 | ||

0x2C6 | ||

0x371 | ||

0x1D5 | ||

0x362 | ||

0x231 | ||

0x111 | ||

0x21B | ||

0x2F8 | ||

0x15C | ||

0x30B | ||

0x3AA | ||

0xBA | ||

0x320 | ||

0x2B7 | ||

0xE1 | ||

0x2D8 | ||

0x1B5 | ||

0x140 | ||

0x131 | ||

0x363 | ||

0xB9 | ||

0x158 | ||

0x3A5 | ||

0x3E | ||

0x3A7 | ||

0x4A | ||

0x171 | ||

0x189 | ||

0x2EE | ||

0x2C6 |

## Table 7

A | B | A + B (in Hex) |
---|---|---|

0x331 | 0x3B6 | |

0x123 | 0x2D4 | |

0x169 | 0x29D | |

0x2DA | 0x29E | |

0x1E3 | 0x2B1 | |

0x8 | 0x200 | |

0x35C | 0xD7 | |

0x23B | 0x1DA | |

0x23A | 0x119 | |

0x3CB | 0x2A8 |

# End of Assignment Checklist

- I finished all the assignments.
- I shared my assignments with others.
- I provided feedback for assignments of at least 2 others.
- I addressed the feedback from others and thanked them for the review.