---
title: "FFH AND C0H; (16)₁₀ − (26)₁₀ by 2's complement"
subject: "Digital Logic"
chapter: 5
key: "semester_3/digital_logic:hex-and-twos-complement-subtract"
source: https://www.bctengineer.com/q/semester_3/digital_logic/hex-and-twos-complement-subtract
site: BCT Engineering
---

# FFH AND C0H; (16)₁₀ − (26)₁₀ by 2's complement

Digital Logic · Chapter 5: Arithmetic Circuits

- Asked in: 2070 Chaitra, 2+2 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/digital_logic/hex-and-twos-complement-subtract
- Whole chapter: https://www.bctengineer.com/md/semester_3/digital_logic/chapter-5

## Question

When FFH is ANDed with C0H what will be the resulting number? Subtract (26)₁₀ from (16)₁₀ using 2's complement binary method.

## Short answer

FFH AND C0H = C0H. For subtraction: 16=00010000, 26=00011010; 2's complement of 26 is 11100110. Add: 00010000+11100110=11110110. No end carry, result is negative; 2's complement of sum is 00001010, so answer is -10.

## Answer

#### FFH AND C0H

AND each bit pair:

```text
 FFH = 1111 1111
 C0H = 1100 0000
 AND = 1100 0000
```

**Answer:** $FF_H \cdot C0_H = C0_H$. (ANDing with $FF_H$ leaves the other number unchanged.)

#### (16)₁₀ − (26)₁₀ by 2's complement (8-bit)

$$
\begin{aligned} 16 &= 0001\,0000 \\ 26 &= 0001\,1010 \\ \text{2's complement of } 26 &= 1110\,0101 + 1 = 1110\,0110 \end{aligned}
$$

```text
   0001 0000   (+16)
 + 1110 0110   (-26)
 -----------
   1111 0110   (no end carry)
```

No end carry, so the result is negative. Its magnitude is the 2's complement of the sum:

$$
\overline{1111\,0110} + 1 = 0000\,1001 + 1 = 0000\,1010 = 10
$$

**Answer:** $16 - 26 = 1111\,0110$ (2's complement form) $= -10$.

## Check yourself

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

1. What is FFH AND C0H?
   A. C0H
   B. FFH
   C. 00H
   D. 3FH
   Answer: A. ANDing with all 1s leaves the other operand unchanged. (Key point: AND with FF)

2. What is the 8-bit 2's complement of 26 (0001 1010)?
   A. 1110 0101
   B. 1110 0110
   C. 0001 1010
   D. 1110 0111
   Answer: B. Invert to 1110 0101 then add 1. (Key point: 2's complement of 26)

3. Adding 16 and the 2's complement of 26 gives 1111 0110. What does it tell us?
   A. End carry, so positive
   B. Overflow
   C. No end carry, so the result is negative
   D. Zero
   Answer: C. With no end carry the answer is negative, magnitude 0000 1010. (Key point: End carry)

4. What is 16 - 26?
   A. 10
   B. -42
   C. -26
   D. -10
   Answer: D. Magnitude is 2's complement of 1111 0110 = 0000 1010 = 10. (Key point: Result)

## Related in Digital Logic

- [Gray code, (11101)Gray to binary, FFH AND CAH](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Agray-to-binary-hex-and) — Digital Logic, chapter 1
- [39 to binary/hex and 2's complement addition](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aconvert-39-binary-hex-addition) — Digital Logic, chapter 1
- [Convert (26.75)₁₀ to binary](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Aconvert-26-75-binary) — Digital Logic, chapter 1
- [Circuit giving 2's complement of a 4-bit number](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Atwos-complement-generator) — Digital Logic, chapter 5
- [Full adder using decoder; (57−43) by 2's complement](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Afull-adder-decoder-subtract) — Digital Logic, chapter 4
- [DEMUX applications; 010 − 011 by 2's complement](https://www.bctengineer.com/question.md?key=semester_3%2Fdigital_logic%3Ademux-applications-subtract) — Digital Logic, chapter 4

## Related in other subjects

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- [2's complement: (1111)2 − (1110)2](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Atwo-complement-1111-1110) — Basic Electronics Engineering, chapter 6