---
title: "Convert octal 623.77 to decimal, binary, hex"
subject: "Digital Logic"
chapter: 1
key: "semester_3/digital_logic:convert-octal-623-77"
source: https://www.bctengineer.com/q/semester_3/digital_logic/convert-octal-623-77
site: BCT Engineering
---

# Convert octal 623.77 to decimal, binary, hex

Digital Logic · Chapter 1: Introduction

- Asked in: 2082 Baisakh, 3 marks
- Video: [Number System Conversion Techniques |Very Easy|Fast |Decimal |Binary|Octal |Hexadecimal| Info pack.](https://www.youtube.com/watch?v=E-Sg2YsvZds) — Info Pack
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/convert-octal-623-77
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-1

## Question

Convert Octal (623.77) to decimal, binary and hexadecimal.

## Short answer

To decimal: 6×8²+2×8+3+7/8+7/64 = 403.984375. To binary: each octal digit to 3 bits gives 110 010 011.111 111. To hexadecimal: regroup binary in 4s from the point → (193.FC)₁₆.

## Answer

#### To decimal

$$
\begin{aligned}
(623.77)_8 &= 6\times8^2 + 2\times8 + 3 + 7\times8^{-1} + 7\times8^{-2} \\
&= 384 + 16 + 3 + 0.875 + 0.109375 \\
&= 403.984375
\end{aligned}
$$

**Decimal: $(403.984375)_{10}$**

#### To binary
Replace each octal digit by 3 bits: 6 = 110, 2 = 010, 3 = 011, 7 = 111, 7 = 111.

**Binary: $(110010011.111111)_2$**

#### To hexadecimal
Regroup the binary into 4 bits from the point:

```text
 Integer : 0001 1001 0011  -> 1 9 3
 Fraction: 1111 1100       -> F C
```

**Hexadecimal: $(193.FC)_{16}$** (check: $403 + 252/256 = 403.984375$)

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. How is octal converted to binary?
   A. Replace each by 4 bits
   B. Replace each octal digit by 3 bits
   C. Divide by 2
   D. Multiply by 8
   Answer: B. 6 = 110, 2 = 010, 3 = 011. (Key point: To binary)

2. What is (623.77) octal in decimal?
   A. 623.77
   B. 413.77
   C. 403.984375
   D. 403.875
   Answer: C. 384 + 16 + 3 + 0.875 + 0.109375. (Key point: To decimal)

3. What is (623.77) octal in hex?
   A. 193.77
   B. 323.FC
   C. 1A3.FC
   D. 193.FC
   Answer: D. Regroup binary in fours: 0001 1001 0011 . 1111 1100. (Key point: To hex)

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