Kenken? That's ken in binary!

Solution

All operations are bitwise. To extract, read the shaded cells in reading order (left to right, top to bottom).

000⊕				111⊕	110⊕
110∧	111⊕		101∨		111⊕		101⊕
					001∧
011∨		001∧		010∧		111MAJ
	100∧	011⊕		001∨			111⊕
		100∧		011∨
100	100⊕		110⊕		100∨		111⊕
110⊕		011MAJ