Number Systems and Data Representation

Computers use four number systems. Binary (Base 2): digits 0,1 — the language of computers. Octal (Base 8): digits 0-7. Decimal (Base 10): digits 0-9 — human system. Hexadecimal (Base 16): digits 0-9 then A,B,C,D,E,F (A=10, B=11... F=15). Memory aid for bases: B-O-D-H = 2-8-10-16. Each binary digit is a 'bit'. A group of 4 bits maps neatly to ONE hex digit (since 2^4=16) and is also a nibble — this is why hex is used as shorthand for binary. Knowing place values (...8,4,2,1 for binary) lets you convert fast. IBPS Clerk keeps conversions small (numbers under 16), so master 0-15 in all four systems.

To convert BINARY to DECIMAL, write place values from right to left as powers of 2: 1, 2, 4, 8, 16, 32... Then add the place values wherever there is a 1. Example: binary 1011 → positions (8 4 2 1) → 1×8 + 0×4 + 1×2 + 1×1 = 8+2+1 = 11. Reverse (DECIMAL to BINARY): repeatedly divide by 2 and read remainders BOTTOM to TOP. Example: 13 → 13/2=6 r1, 6/2=3 r0, 3/2=1 r1, 1/2=0 r1 → read up = 1101. Speed tip: memorise 8-4-2-1 columns; any number 0-15 fits in 4 bits. Quick checks: 1111=15, 1000=8, 1010=10.

Computers store characters using coding schemes. ASCII (American Standard Code for Information Interchange) uses 7 or 8 bits, representing 128 (or 256 extended) characters — capital 'A' = 65, 'a' = 97, '0' = 48. EBCDIC (8-bit) was used on IBM mainframes. UNICODE uses up to 16/32 bits and can represent characters of almost ALL world languages (including Hindi, Chinese, emojis) — over 1 lakh characters. Memory hook: ASCII = English/basic, Unicode = Universal/all languages. BCD (Binary Coded Decimal) represents each decimal digit by 4 bits. For IBPS Clerk: remember ASCII 'A'=65 and that Unicode is the universal standard supporting Indian languages.

Cover the answer, recall, then check. 12 cards on number systems and codes for IBPS Clerk.

Q1. State the base (radix) of Binary, Octal, Decimal and Hexadecimal.
A1. Binary = 2, Octal = 8, Decimal = 10, Hexadecimal = 16.

Q2. Which digits/symbols are valid in each system?
A2. Binary: 0-1; Octal: 0-7; Decimal: 0-9; Hexadecimal: 0-9 and A-F.

Q3. In hexadecimal, what decimal values do A, C and F represent?
A3. A = 10, C = 12, F = 15.

Q4. Convert binary (1010)₂ to decimal.
A4. 8+0+2+0 = 10.

Q5. What do MSB and LSB mean?
A5. MSB = Most Significant Bit (leftmost); LSB = Least Significant Bit (rightmost).

Q6. Expand ASCII and give its bit size.
A6. American Standard Code for Information Interchange; standard 7-bit (128 chars), extended 8-bit (256 chars).

Q7. Which coding scheme is universal and supports all world languages?
A7. Unicode (commonly 16-bit), which can represent characters of every language.

Q8. Expand EBCDIC and name the company that uses it.
A8. Extended Binary Coded Decimal Interchange Code; an 8-bit code used by IBM mainframes.

Q9. Convert decimal 8 to binary.
A9. (1000)₂.

Q10. How many values can be represented by n bits?
A10. 2ⁿ values (e.g., 8 bits = 2⁸ = 256 values).

Q11. What is a bit and a byte?
A11. Bit = Binary digIT (0 or 1); Byte = 8 bits, the basic unit for one character.

Q12. Convert hexadecimal (1F)₁₆ to decimal.
A12. 1×16 + 15 = 31.

Worked Example

Problem: Solved computation: Convert the decimal number 25 into its binary equivalent.

Solution:
Divide repeatedly by 2 and record remainders from bottom to top.
25 ÷ 2 = 12 remainder 1
12 ÷ 2 = 6 remainder 0
6 ÷ 2 = 3 remainder 0
3 ÷ 2 = 1 remainder 1
1 ÷ 2 = 0 remainder 1
Reading remainders upward: 11001.
Check: 16 + 8 + 0 + 0 + 1 = 25 ✓.

Answer: (25)₁₀ = (11001)₂.