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--- tanszek:oktatas:techcomm:encoding_integers [2024/09/30 18:17] – created knehez
+++ tanszek:oktatas:techcomm:encoding_integers [2024/09/30 18:54] (current) – [How to convert decimal integers to binary form] knehez
@@ Line 38: / Line 38: @@
   * Invert the bits: **11111010**
   * Add one: **11111011**
+**Example**: Add -5 + 7 in 8 bits binary format
+Now we can add the two binary numbers:
+<code>
+  11111011   (-5 in two's complement)
++ 00000111   (7)
+------------
+  00000010   (2)
+</code>
+This is the reason why we are using the special two's complement form. Without using this encoding, we cannot add negative and positive numbers.
+==== How to convert decimal integers to binary form ====
+Let’s convert the decimal number **156** into binary.
+==== Step 1: Divide the decimal number by 2 ====
+Start by dividing the decimal number (156) by 2 and keep track of the quotient and remainder. The remainder will be either 0 or 1, which forms the binary digits from bottom to top.
+| **Division** | **Quotient** | **Remainder** |
+| 156 ÷ 2          | 78       | 0         |
+| 78 ÷ 2           | 39       | 0         |
+| 39 ÷ 2           | 19       | 1         |
+| 19 ÷ 2           | 9        | 1         |
+| 9 ÷ 2            | 4        | 1         |
+| 4 ÷ 2            | 2        | 0         |
+| 2 ÷ 2            | 1        | 0         |
+| 1 ÷ 2            | 0        | 1         |
+==== Step 2: Write the binary digits ====
+To get the binary representation, take the remainders from bottom to top. The binary equivalent of **156** is:
+**10011100₂**
+==== Verification ====
+To verify, we can convert the binary number back to decimal:
+  (1 × 2⁷) + (0 × 2⁶) + (0 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (0 × 2¹) + (0 × 2⁰)
+  = 128 + 0 + 0 + 16 + 8 + 4 + 0 + 0
+  = 156
+Hence, the binary representation of 156 is correct.