Identify both the mask and the logical operation needed to accomplish each of the following objectives: a. Put 1s in the upper 4 bits of an 8-bit pattern without disturbing the other bits. b. Complement the most significant bit of an 8-bit pattern without changing the other bits. c. Complement a pattern of 8 bits. d. Put a 0 in the least significant bit of an 8-bit pattern without disturbing the other bits. e. Put 1s in all but the most significant bit of an 8-bit pattern without disturbing the most significant bit. f. Filter out all of the green color component from an RGB bitmap image pixel in which the middle 8 bits of a 24-bit pattern store the green information. g. Invert all of the bits in a 24-bit RGB bitmap pixel. h. Set all the bits in a 24-bit RGB bitmap pixel to 1, indicating the color “white”.
The Correct Answer and Explanation is:
a. Set 1s in the upper 4 bits of an 8-bit pattern (bits 7–4), without disturbing the other bits.
- Mask:
0xF0(11110000) - Operation: OR
- Explanation: OR-ing with 1 sets a bit to 1, while OR-ing with 0 keeps it unchanged. So
pattern | 0xF0sets the upper 4 bits to 1.
b. Complement the most significant bit (bit 7) of an 8-bit pattern.
- Mask:
0x80(10000000) - Operation: XOR
- Explanation: XOR-ing a bit with 1 flips it. Only bit 7 is affected using this mask.
c. Complement an entire 8-bit pattern.
- Mask:
0xFF(11111111) - Operation: XOR
- Explanation: XOR-ing every bit with 1 flips all bits. Equivalent to
~pattern.
d. Put a 0 in the least significant bit (bit 0) of an 8-bit pattern without disturbing other bits.
- Mask:
0xFE(11111110) - Operation: AND
- Explanation: AND-ing with 0 clears a bit. All other bits AND with 1 stay unchanged.
e. Set all bits except the most significant bit to 1 (bits 6–0), preserving bit 7.
- Mask:
0x7F(01111111) - Operation: OR
- Explanation: OR-ing with 1 sets bits to 1. Bit 7 (most significant) is OR-ed with 0 and remains unchanged.
f. Filter out the green component (middle 8 bits) from a 24-bit RGB pixel.
- Mask:
0xFF00FFFF - Operation: AND
- Explanation: Set green bits (bits 8–15) to 0 and preserve red (bits 16–23) and blue (0–7) components.
g. Invert all bits in a 24-bit RGB pixel.
- Mask:
0xFFFFFF - Operation: XOR
- Explanation: XOR with 1 flips each bit. So
pixel ^ 0xFFFFFFinverts all 24 bits.
h. Set all bits in a 24-bit RGB pixel to 1 (white).
- Mask:
0xFFFFFF - Operation: OR
- Explanation: OR-ing any bit with 1 sets it to 1. All 24 bits become 1, resulting in white (
0xFFFFFF).
Summary (Explanation):
Bit masking is a core technique in low-level programming for modifying or analyzing specific bits in data. Operations like AND, OR, and XOR help us isolate, set, or flip particular bits. AND is used to clear bits, OR to set bits, and XOR to toggle bits. Proper masking ensures we modify only the intended bits. This technique is vital in embedded systems, graphics, and networking applications where memory and performance are critical.
