Video summary

Hexadecimal to Binary & Binary to Hexadecimal Conversion

Main summary

Key takeaways

Educational

Main Ideas / Concepts

  • Hexadecimal number system

    • Uses base 16, meaning there are 16 digits: values 0 through 15.
    • Digits 10–15 are represented as:
      • 10 = A, 11 = B, 12 = C, 13 = D, 14 = E, 15 = F

  • Core conversion rule (hex ↔ binary)

    • Each hexadecimal digit corresponds to exactly 4 bits (4-bit binary).
    • This is analogous to how octal digits map to 3 bits, but here the group size is 4 bits.

Methodology / Step-by-Step Instructions

A) Convert Hexadecimal → Binary

  • Use a mapping table where each hex digit corresponds to 4 bits:
    • 0 = 0000
    • Continue through 1, 2, …, F = 1111
  • For each hexadecimal digit in the number:
    • Replace it with its 4-bit binary equivalent.
  • Handle integer and fractional parts:
    • Convert the integer part digit-by-digit using the 4-bit mapping.
    • Convert the fractional part digit-by-digit using the same 4-bit mapping.
    • Keep the binary point aligned where appropriate (the video converts parts separately around the point).

Example shown (Hex → Binary)

  • Input hex: 259A

  • Output binary (as stated): 0010 0101 1001 1010 (binary point is not shown in the example’s displayed form)

  • Another example:

    • Input: CAFE.3D
    • Convert each hex digit to 4-bit binary, including fractional digits after the .

B) Convert Binary → Hexadecimal

Steps

  1. Identify the binary point.
  2. Group bits into sets of 4
    • For the integer part: group from right to left.
    • For the fractional part: group from left to right.
  3. Pad with zeros if needed
    • If a group has fewer than 4 bits, add:
      • Leading zeros (left side) or
      • Trailing zeros (right side)
    • The video emphasizes that adding zeros on the left or right does not change the value.
  4. Convert each 4-bit group to its hex digit
    • Use the same conceptual 4-bit mapping table. Examples mentioned:
      • 1000 = 8
      • 1001 = 9
      • 1100 = C
  5. Reconstruct the hex number
    • Combine the hex digits in order, placing the hexadecimal point where the binary point mapping implies.

Example shown (Binary → Hex)

  • Input binary (as shown): 1010 0111 . 1? (subtitle formatting is compressed, but the grouping method is clear)

  • After grouping into 4-bit chunks, the final hexadecimal result is stated as:

    • 89.C

Padding follow-up example

  • If there is one extra bit (not enough to form a full group), pad with three zeros to make a 4-bit group.
    • In that case, 0001 = 1
  • The final stated result for the modified case:
    • 189C

Homework / Tasks Assigned

  • Homework 1: Convert the hexadecimal number FACE to its binary equivalent.
  • Homework 2: Convert the binary number 1101111010111111 to its hexadecimal equivalent.

Speakers / Sources

  • No specific speaker name is provided in the subtitles.
  • The speaker is an unnamed instructor/lecturer.

Original video